Instructional Materials for the WCSD Math Common Finals
|
|
- Ferdinand Hoover
- 5 years ago
- Views:
Transcription
1 Geometry Semester 2 Instructional Materials for the WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Math Common Final blueprint for this course. When used as test practice, success on the Instructional Materials does not guarantee success on the district math common final. Students can use these Instructional Materials to become familiar with the format and language used on the district common finals. Familiarity with standards vocabulary and interaction with the types of problems included in the Instructional Materials can result in less anxiety on the part of the students. Teachers can use the Instructional Materials in conjunction with the course guides to ensure that instruction and content is aligned with what will be assessed. The Instructional Materials are not representative of the depth or full range of learning that should occur in the classroom Note from Earl. Many of the solutions in this document use techniques presented in the Geometry Handbook, which is available on the website. If you have trouble following any of the techniques used, try looking in the handbook for pages that deal with the issue you are struggling with. I solve the problems in this sample test using the quickest method available in most cases. Occasionally, I also make comments about some of the math involved in an effort to enhance your understanding of what is going on in the problem. You may have learned different techniques in your classroom. Use whichever techniques work for you. Finally, if there is a conflict between the content of this document and what you have learned in class, your teacher should be the primary source for how any problem should be solved. 1 Page
2 Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale. 1. The ratios of the areas of square A to square B is. If the area of square B is 100, what is the length of a side of square A? A. 4 C. 10 B. 8 D. 64 For this kind of problem, we set up a proportion, with the ratio of the areas on one side and the actual areas on the other Cross multiply the two fractions to get: Then: 64. We are not yet finished because the problem asks for the length of the side of Square. For this, we use the area formula, where represents the length of a side: 64, which we solve to obtain. Answer B 2. What is the scale factor for the dilation of to image? A. 2 B. 1 C. 2 D. 3 To determine the scale factor of a dilation from the origin, pick corresponding points on the two figures and divide the and values of the image by those of the pre image. If the two values that result are the same, you have most likely determined the scale factor without error. I have selected Points 1, 4 and 3, 12 for this purpose Page
3 Since the calculated scale factors are both, I can conclude with confidence that Answer D is correct. 3. Apply the dilation :, 4, 4 to the polygon with the given vertices. Name the coordinates of the image points. A. 8, 4, 16, 4, 16, 12 B. 8, 4, 16, 4, 16, 12 C. 0.5, 0.25, 1, 0.25, 1, 0.75 D. 0.5, 0.25, 1, 0.25, 1, 0.75 Determine the coordinates of the points; then apply the dilation, as follows: 2,1 4,1 4, , 4 1 8, 4 4, ,4 4, , 12 Answer A 4. The pair of triangles is similar. What is the value for? A. 18 B. 16 C. 13 D. 3 To help with this problem, let s assign some letters to the vertices of the two triangles. Then, we note that ~ by following the angle congruences from angle to angle ( ; ; ). is the measure of side, so we want it in our proportion. Then, using corresponding sides, we have: Answer A The following page contains information about the similarity theorems from the Geometry Handbook available at 3 Page
4 Geometry Similar Triangles The following theorems present conditions under which triangles are similar. Side Angle Side (SAS) Similarity Side Side Side (SSS) Similarity SAS similarity requires the proportionality of two sides and the congruence of the angle between those sides. Note that there is no such thing as SSA similarity; the congruent angle must be between the two proportional sides. SSS similarity requires the proportionality of all three sides. If all of the sides are proportional, then all of the angles must be congruent. Angle Angle (AA) Similarity AA similarity requires the congruence of two angles and the side between those angles. Similar Triangle Parts In similar triangles, Corresponding sides are proportional. Corresponding angles are congruent. Establishing the proper names for similar triangles is crucial to line up corresponding vertices. In the picture above, we can say: ~ or ~ or ~ or ~ or ~ or ~ All of these are correct because they match corresponding parts in the naming. Each of these similarities implies the following relationships between parts of the two triangles: and and 4 Page
5 5. In the figure, ~. What is the length of side? A. 6 B. 7 C. 16 D. 20 Note the angle congruences that result from the parallel lines: and Then, we note that ~ from the AA Similarity Theorem. Then, using corresponding sides, we have the following proportion: Finally, we want to determine: AB Answer D 6. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1. Which statement regarding the two triangles is not true? A. Their areas have a ratio of 4: 1 B. The scale factor is a ratio of 2: 1 C. Their perimeters have a ratio of 2: 1 D. Their corresponding angles have a ratio of 2: 1 Some thoughts: If the ratio of side lengths is : in a pair of similar figures. Then: The measures of the angles in the two figures are the same. The ratio of any one dimensional measurements is :. The ratio of any two dimensional measurements (e.g., areas) is : The ratio of any three dimensional measurements (e.g., volumes) is : Relating these rules to this problem, we note that the scale factor is one dimensional, so A, B, and C are all true. D is false because the angle measures in the triangles are the same. Answer D 5 Page
6 7. What is the value of? A. 39 B. 54 C. 63 D. 90 To help with this problem, let s assign some letters to the vertices of the two triangles. Then, we note that ~. is the measure of side, so we want it in our proportion. Using corresponding sides, we have: Answer D 8. In, is the midpoint of, is the midpoint of, and R is the midpoint of. Given the following, what is the perimeter of? A B C D The Perimeter of is: following: (given) 8.2. Since points, and are midpoints, we have the The perimeter then is: Answer B 6 Page
7 9. In the figure, is a right triangle and ~. What is the length of? A. 20 B. 40 C D There are special rules for these three triangle problems, which may be learned as words instead of formulas. I list all three here because the problem on the final may involve different parts of the three triangles. The height squared = the product of: the two parts of the base The left side squared = the product of: the part of the base below it and the entire base The right side squared = the product of: the part of the base below it and the entire base Using the first column of this table, we have: or Then, taking the square root of both sides of the equation, we get:. Answer C 10. In the right triangle, and represent unknown side lengths. What is the length of side? A. 2 B. 4 C. 2 3 D. 3 2 In a Triangle, the proportions of the sides are: : : for short side : long side : hypotenuse respectively. In this problem, we are given the short side and asked to calculate the hypotenuse. The length of the hypotenuse is two times the length of the short side. So, we have: 2 2. Answer B 7 Page
8 11. In the figure, what is the distance a ball travels when thrown from second base to home plate? A. 90 B. 180 C D In a Triangle, the proportions of the sides are: : : for side : side : hypotenuse respectively. In this problem, we are given the two sides and asked to calculate the hypotenuse. The length of the hypotenuse is 2 times the size of the length of a side. So, we have: 2 90 feet. Answer C 12. What is cos in the triangle? A C B D SOH CAH TOA sin cos tan In this problem: cos Answer A 8 Page
9 13. What is the value of in the triangle? A. 16 cos 35 cos 35 B. 16 C. 16 sin 35 D. 16 sin 35 Using SOH CAH TOA, we first note that relative to the angle of 35, we are given the opposite side and the hypotenuse. The trig function that uses these two sides is the sine function. So, sin 35 sin x 16 sin 35 Answer D 14. What is the measure of angle A in the triangle, rounded to the nearest degree? A. 35 B. 44 C. 46 D. 72 Using SOH CAH TOA, we first note that relative to angle, we are given the adjacent side and the hypotenuse. The trig function that uses these two sides is the cosine function. So, cos cos ~ (using a calculator) Answer C 9 Page
10 15. A person is standing at ground level with the base of the Empire State Building in New York City. The angle formed by the ground and a line segment from his position to the top of the building is The height of the Empire State Building is 1472 feet. Find the distance that he is standing from the base of the Empire State Building to the nearest foot. A. 8 C B D We need a picture for this one, so I drew the one to the right. Using SOH CAH TOA, we first note that relative to the 48.4 angle, we are given the adjacent side and the opposite side. The trig function that uses these two sides is the tangent function. So, t an 48.4,,. ~, Answer B 16. In the figure, is a right triangle with the hypotenuse. Given the segments lengths of 5, 4,2,and 1, what is cos? A. 5 C. 5 5 B D I have added the given dimensions to the diagram, as You should on any problem that gives lengths or angles. Next, notice that calculating the cosine of angle B requires us to use only at the right. Using SOH CAH TOA, cos, but we do not want to leave a radical in the denominator, so, cos Answer C 10 Page
11 17. Using a string a student decided to determine the diameter of a large trash can. If a string 60 long will wrap around the trash can, what is the approximate diameter of the trash can? A. 25 C B D. 9 Drawing a picture of the situation helps see the one at right. Next, we need the formula for circumference in terms of diameter: In this problem, 60, so we get: 60 ~. inches Answer B 18. A rectangle is inscribed in a circle as shown below. Find the exact circumference of the circle. A. 13 B. 17 C. 119 D. 169 Draw the diameter in the picture to the right. Calculate using the Pythagorean Theorem: Taking the square root of both sides gives: 13. Next, we need the formula for circumference in terms of diameter: In this problem, 13, so we get: 13 mm Answer A 11 Page
12 19. What is the area of a regular hexagon with an apothem of 10 and a side length of? A B C D. 600 We need the formula for area of a regular polygon based on the apothem and side length:, where: length of apothem, perimeter of the regular polygon. In this problem, 10 and , so we get: cm 2 Answer A 20. Given that the side of the regular pentagon is 8 and that the apothem is approximately 5.51, what is the approximate area of the shaded triangle? A. 20 B. 22 C. 64 D. 110 We want the area of the shaded region, which is a triangle. So, we will use the formula for area of a triangle., where: length of the base, height of the triangle. Note that the base of the triangle is the length of a side of the polygon ( 8 ft. ). Also, the height of the triangle is the length of the apothem (5.51 ft.). In this problem, 8 and 5.51, so we get: ~ ft 2 Answer B 12 Page
13 21. If two pieces of ice have the same volume, the one with the greater surface area will melt faster because more of its surface area is exposed to the air, which is warmer than the ice. Two pieces of ice labeled and B have the same volume. Each piece of ice is shaped like a rectangular prism. Which piece of ice melts the fastest? A. Piece melts the fastest. B. Piece melts the fastest. C. They take the same amount of time to melt. D. A relationship cannot be determined First check that the volumes are equal: ft ft 3 Since the volumes are equal, we can check the surface areas: ft ft 2 The one that melts fastest is the one with the greatest surface area, which is Piece. Answer A 22. What best describes the cross section shown on the cube? A. square C. trapezoid B. triangle D. rectangle The cross section shown is a quadrilateral. It appears to have two parallel sides (the top and bottom) and two non parallel sides (the left and right). This describes a trapezoid. Answer C The following page contains information about the various kinds of quadrilaterals from the Geometry Handbook available at 13 Page
14 Geometry Figures of Quadrilaterals Kite 2 consecutive pairs of congruent sides 1 pair of congruent opposite angles Diagonals perpendicular Trapezoid 1 pair of parallel sides (called bases ) Angles on the same side of the bases are supplementary Isosceles Trapezoid 1 pair of parallel sides Congruent legs 2 pair of congruent base angles Diagonals congruent Parallelogram Both pairs of opposite sides parallel Both pairs of opposite sides congruent Both pairs of opposite angles congruent Consecutive angles supplementary Diagonals bisect each other Rectangle Parallelogram with all angles congruent (i.e., right angles) Diagonals congruent Rhombus Parallelogram with all sides congruent Diagonals perpendicular Each diagonal bisects a pair of opposite angles Square Both a Rhombus and a Rectangle All angles congruent (i.e., right angles) All sides congruent 14 Page
15 23. A layered cake is a solid of revolution. Which of the following is the drawing of a twodimensional shape and an axis of rotation that could form the cake? A. C. B. D. Rotating a straight edge creates a circular shape in three dimensions. We want half of the shape that we see looking at a cross section of the cake in 2 dimensions. Answer D 24. What is the volume of the cylinder in terms of x? A B C D We need the formula for volume of a cylinder based on the radius of a base and the height:, where: radius of a base, height of the cylinder. In this problem, 3 and 54, so we get: cm 3 Answer C The following page contains formulas for the volumes and surface areas for various solids from the Geometry Handbook available at 15 Page
16 Geometry Summary of Surface Area and Volume Formulas 3D Shapes Shape Figure Surface Area Volume Sphere Right Cylinder Cone Square Pyramid Rectangular Prism Cube General Right Prism 16 Page
17 25. What is the height of a square pyramid that has a side length of 13 and a volume of 1521? A. 3 C. 27 B. 9 D. 39 We need the formula for volume of a square pyramid based on the length of a side of the base and the height:, where: length of a side of the base, height of the pyramid. In this problem, 13 and 1,521, so we get: 1, ,521 Solving for, we get:, ft. Answer C 26. A food manufacturer sells yogurt in cone shaped cups with the dimensions shown. To the nearest tenth, how many fluid ounces of yogurt does the cup hold? (Hint: ) A. 0.6 B. 5.7 C D We need the formula for volume of a cone based on the radius of the base and the height:, where: radius of a base, height of the cone. In this problem, 824 and 10, so we get: ~ cm3 In fluid ounces, this is ~ ~. fl. oz. Answer B 17 Page
18 27. What is the volume of the sphere in terms of? A. 36 B. 48 C. 288 D. 864 We need the formula for volume of a sphere based on the radius of the sphere:, where: radius of the sphere. In this problem, 6, so we get: ft 3 Answer C 28. You want to design a cylindrical container for oatmeal that has a volume of 77. You also want the height of the container to be 2 times the radius. To the nearest tenth, what should the radius of the container be? A. 2.3 B. 2.9 C. 3.0 D. 3.1 We need the formula for volume of a cylinder based on the radius of a base and the height:, where: radius of a base, height of the cylinder. In this problem, 77, and 2, so we get: , and solving for gives: ~. inches Answer A 18 Page
19 29. Find the volume of the composite figure. Round your answer to the nearest tenth. A. 245 B. 441 C. 539 D. 735 The volume of the composite figure is the sum of the volumes of the square pyramid on top, and the rectangular prism on the bottom. For the square pyramid: m 3 For the rectangular Prism: m 3 Total volume is: m 3 Answer C 30. What is the ratio of the volumes of the two cubes? The cubes have edges of lengths 3 inches and 12 inches. A. 1: 4 B. 1: 16 C. 1: 64 D. 1: 256 Some thoughts: If the ratio of side lengths is : in a pair of similar figures. Then: The measures of the angles in the two figures are the same. The ratio of any one dimensional measurements is :. The ratio of any two dimensional measurements (e.g., areas) is : The ratio of any three dimensional measurements (e.g., volumes) is : In this problem, the ratios of the lengths is 3: 12, which simplifies to 1: 4. Then, the ratio of the volumes is: 1 :4 : Answer C Note that the ratio of the surface areas is: 1 :4 1:16. Watch out for a question like this on the real final. 19 Page
20 31. Given mac = mbc and is a central angle, what is the value of and mbc? A. 18, mbc 136 B. 9.2, mbc 88 C. 18, mbc 88 D. 9.2, mbc 136 Let s add a couple of indicators (orange dashes) for measures that are equal. Now, let s work with the arc and angle shown. Recall that the measure of an inscribed angle is half the measure of the arc it subtends. This tells us that: Solving for x, we get: (Note also that ) To determine, note that: 360 (the whole circle) Since 88 and, we can convert the above equation to: or Solving for gives us. Answer A 32. What is the measure of angle x? A. 50 B. 35 C. 25 D. 5 An angle with a vertex outside the circle is half the difference of its subtended arcs Answer C The following pages contain information about circles, angles and their subtended arcs from the Geometry Handbook available at 20 Page
21 Geometry Parts of Circles Center the middle of the circle. All points on the circle are the same distance from the center. Radius a line segment with one endpoint at the center and the other endpoint on the circle. The term radius is also used to refer to the distance from the center to the points on the circle. Diameter a line segment with endpoints on the circle that passes through the center. Arc a path along a circle. Minor Arc a path along the circle that is less than 180⁰. Major Arc a path along the circle that is greater than 180⁰. Semicircle a path along a circle that equals 180⁰. Sector a region inside a circle that is bounded by two radii and an arc. Secant Line a line that intersects the circle in exactly two points. Tangent Line a line that intersects the circle in exactly one point. Chord a line segment with endpoints on the circle that does not pass through the center. 21 Page
22 Geometry Angles and Circles Central Angle Inscribed Angle Vertex inside the circle Vertex outside the circle Tangent on one side Tangents on two sides 22 Page
23 33. What is the measure of RS? A. 54 B. 38 C. 32 D. 27 An angle with a vertex inside the circle is half the sum of its subtended arcs Answer C 34. What is the measure of the inscribed angle, if the ray is tangent to the circle? A. 140 B. 110 C. 70 D. 55 Arc measure is: This is a special case of the measure of an inscribed angle. Recall that the measure of an inscribed angle is half the measure of the arc it subtends. The arc we care about is the one for which the measure is not given in the problem. We must calculate it, as show above in magenta, to be. Then, 220 Answer B 23 Page
24 35. What is the length of the minor arc AB in the circle with a radius of 36? A. 9 B. 6 C D. 1.5 First, let s get the circumference of the whole circle: Next, let s find out what part of the whole circle is represented by the arc. The arc is 30 out of a total of 360 in a complete circle. This is of the whole circle. Multiply these two values together to get the length of minor arc. 72 cm. Answer B 36. What is the area of a circular pool that has a circumference of 100? A. 10 C. 100 B. 50 D First, find the radius of the pool from the circumference ft. Next, calculate the area of the circle from the formula: 50 ft 2 Answer D The following page contains information about arc length and sector area from the Geometry Handbook available at 24 Page
25 Geometry Circle Lengths and Areas Circumference and Area is the circumference (i.e., the perimeter) of the circle. is the area of the circle. where: is the radius of the circle. Length of an Arc on a Circle A common problem in the geometry of circles is to measure the length of an arc on a circle. Definition: An arc is a segment along the circumference of a circle. where: AB is the measure (in degrees) of the arc. Note that this is also the measure of the central angle. is the circumference of the circle. Area of a Sector of a Circle Another common problem in the geometry of circles is to measure the area of a sector a circle. Definition: A sector is a region in a circle that is bounded by two radii and an arc of the circle. where: AB is the measure (in degrees) of the arc. Note that this is also the measure of the central angle. is the area of the circle. 25 Page
26 37. The diameter of a circular pizza pan is 18. Two-thirds of the pizza is eaten by your friends. What is the approximate area of the pizza pan that is covered by the remaining pizza? (Assume that the diameter of the pan and the diameter of the pizza are the same.) A. 170 C. 54 B. 85 D. 27 If your friends eat of a pizza, there is left for you. Note also that the radius of the pizza pan is The area of the whole pizza is: 9 81 in 2 9 inches. The portion of the pizza left for you, then, is: ~ in2 Answer B 38. A sector of a circle has an area of 75 and an arc measure of 120. What is the radius of the circle? A C. 5 B D. 15 First, let s find out what part of the whole circle is represented by the arc. The arc is 120 out of a total of 360 in a complete circle. This is of the whole circle. So, the Area of the circle must be three times the size of the sector: The radius of the circle can then be determined from the area formula: cm Answer D 26 Page
27 39. Given the circle inscribed in the square with side length 12. What is the probability that the point lies inside the circle, if a point is chosen at random inside the square? A. C. B. 1 D. 4 4 The probability is the ratio of the shaded area to the total area. Note that the radius of the circle is half the length of the side of the square: 6 Answer D 40. Find the probability that a point chosen at random in the trapezoid shown lies in either of the shaded regions. Round your answer to the nearest hundredth. A B C D The probability is the ratio of the shaded area to the total area. I have added a couple of measurements to the above diagram to make the calculations easier. ~. Answer C The following page contains information regarding perimeters and areas of 2 dimensional shapes from the Geometry Handbook available at One interesting thing to keep in mind is that a square is also a kite. So if you are given the diagonal of a square and asked to find the area, use the formula 27 Page
28 Geometry Summary of Perimeter and Area Formulas 2D Shapes Shape Figure Perimeter Area Kite,, Trapezoid Parallelogram,,, b,b bases h height Rectangle, Rhombus, Square, Regular Polygon Circle 28 Page
29 41. A grab bag contains 7 football cards and 3 basketball cards. An experiment consists of taking one card out of the bag, then selecting another card. What is the probability of selecting a football card, replacing it, and then selecting a basketball card? A C B D Let s look at the probabilities for a draw. Notice that the probabilities don NOT change after the first draw because you replace the card chosen. Cards Probability Football Cards 7 7/ Basketball Cards 3 3/ Total Cards 10 Notice that the two draws are independent of each other. Two events are independent when neither one affects the other. When events are independent, we can multiply the probabilities of each event to get the overall probability Answer C 42. A bag contains hair ribbons for a spirit rally. The bag contains 5 black ribbons and 7 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. Find the probability that both events and occur. A. :. : B C D Let s look at the probabilities for each draw. Notice that the probabilities change after the first draw because you do not replace the ribbon chosen. Lila Draw Jessica Draw Black Ribbons 5 4 Green Ribbons 7 7 Total Ribbons Notice that the probabilities change between the two draws because they are not independent. We still multiply the two resulting probabilities. Answer C 29 Page
30 43. The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Which is the correct answer as a fraction in simplest form? Left-handed Right-handed Total Male 2 35 Female A. 3 4 B. 1 7 C. 1 6 D We are given that the student is female, so we confine ourselves to that row. I added the total column so we can do our calculation: 6 42 Answer B 44. The table shows the distribution of the labor force in a city in the year Suppose that a worker is selected at random. Find the probability of randomly selecting a worker in the Industry field given that the worker is female. Which is the correct answer as a decimal rounded to the nearest thousandth? Agriculture Industry Services Total Male 3,132 25,056 50,112 Female 667 8,004 57,362 66,033 A B C D We are given that the worker is female, so we confine ourselves to that row. I added the total column so we can do our calculation: 8, 004 ~. 66,033 Answer C 30 Page
31 45. Events and are independent. Find the missing probability. (call it ) A. 0.7 C. 0.2 B D. 0.3 If two events are independent, then. For this problem, 0.06 Solving for, we get... Answer 0.3 C 46. If 0.43 and 0. 89, find. A C B D The key formula to use here is: ~. Answer D 47. The sections on a spinner are numbered from 1 through 8. If the probability of landing on a given section is the same for all the sections, what is the probability of spinning a number less than 4 or greater than 7 in a single spin? A. B. The successes are values 4or 7. So, 1,2,3,8. There are 4 possible successes out of a set of 8 total possibilities when spinning. The resulting probability of success is: C. D Answer A 31 Page
32 48. Given, a student constructed point as shown. Next the student will draw a circle with center and radius. Which statement is true and why? A. Circle will be inscribed in because point is the intersection of two angle bisectors of. B. Circle will be circumscribed about because point is the intersection of two angle bisectors of. C. Circle will be circumscribed about because point is the intersection of two perpendicular bisectors of sides of. D. Circle will be inscribed in because point is the intersection of two perpendicular bisectors of sides of. The center of the circle (O) in this problem is the intersection of angle bisectors of the triangle. This point of intersection is called the incenter of the triangle. The incenter is also the center of the circle inscribed in the triangle. The key words in the paragraph above are angle bisectors and inscribed. These are the words in Answer A. The following page contains information regarding other centers of triangles with which the student should be familiar. The page is from the Geometry Handbook available at: 32 Page
33 Geometry Centers of Triangles The following are all points which can be considered the center of a triangle. Centroid (Medians) The centroid is the intersection of the three medians of a triangle. A median is a line segment drawn from a vertex to the midpoint of the line opposite the vertex. The centroid is located 2/3 of the way from a vertex to the opposite side. That is, the distance from a vertex to the centroid is double the length from the centroid to the midpoint of the opposite line. The medians of a triangle create 6 inner triangles of equal area. Orthocenter (Altitudes) The orthocenter is the intersection of the three altitudes of a triangle. An altitude is a line segment drawn from a vertex to a point on the opposite side (extended, if necessary) that is perpendicular to that side. In an acute triangle, the orthocenter is inside the triangle. In a right triangle, the orthocenter is the right angle vertex. In an obtuse triangle, the orthocenter is outside the triangle. Circumcenter (Perpendicular Bisectors) The circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. A perpendicular bisector is a line which both bisects the side and is perpendicular to the side. The circumcenter is also the center of the circle circumscribed about the triangle. In an acute triangle, the circumcenter is inside the triangle. In a right triangle, the circumcenter is the midpoint of the hypotenuse. In an obtuse triangle, the circumcenter is outside the triangle. Euler Line: Interestingly, the centroid, orthocenter and circumcenter of a triangle are collinear (i.e., lie on the same line, which is called the Euler Line). Incenter (Angle Bisectors) The incenter is the intersection of the angle bisectors of the three angles of the triangle. An angle bisector cuts an angle into two congruent angles, each of which is half the measure of the original angle. The incenter is also the center of the circle inscribed in the triangle. 33 Page
34 49. Find the angle measures of. A B C D Opposite angles of a quadrilateral inscribed in a circle add to 180. So, we have: Solving for, we get: 34. Then, substitute 34 into the measures of each angle to get our solution: These two angles add to Finally, Answer B 34 Page
35 50. Which circle is inscribed in the triangle? A. Circle B. Circle C. Circle D. All of the above Inscribed means inside the triangle. So that would be Circle. Answer A Geometry Semester 2 Instructional Material Answers 1. B 11. C 21. A 31. A 41. C 2. D 12. A 22. C 32. C 42. C 3. A 13. D 23. D 33. C 43. B 4. A 14. C 24. C 34. B 44. C 5. D 15. B 25. C 35. B 45. C 6. D 16. C 26. B 36. D 46. D 7. D 17. B 27. C 37. B 47. A 8. B 18. A 28. A 38. D 48. A 9. C 19. A 29. C 39. D 49. B 10. B 20. B 30. C 40. C 50. A 35 Page
Geometry Final Exam - Study Guide
Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are
More informationPostulates, Theorems, and Corollaries. Chapter 1
Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a
More informationALLEGHANY COUNTY SCHOOLS CURRICULUM GUIDE
GRADE/COURSE: Geometry GRADING PERIOD: 1 Year Course Time SEMESTER 1: 1 ST SIX WEEKS Pre-Test, Class Meetings, Homeroom Chapter 1 12 days Lines and Angles Point Line AB Ray AB Segment AB Plane ABC Opposite
More informationVideos, Constructions, Definitions, Postulates, Theorems, and Properties
Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording
More informationGeometry: Semester 2 Practice Final Unofficial Worked Out Solutions by Earl Whitney
Geometry: Semester 2 Practice Final Unofficial Worked Out Solutions by Earl Whitney 1. Wrapping a string around a trash can measures the circumference of the trash can. Assuming the trash can is circular,
More informationGeometry Practice. 1. Angles located next to one another sharing a common side are called angles.
Geometry Practice Name 1. Angles located next to one another sharing a common side are called angles. 2. Planes that meet to form right angles are called planes. 3. Lines that cross are called lines. 4.
More informationGeometry Vocabulary Math Fundamentals Reference Sheet Page 1
Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and
More informationGeometry CP Pen Argyl Area High School 2018
Geometry emphasizes the development of logical thinking as it relates to geometric problems. Topics include using the correct language and notations of geometry, developing inductive and deductive reasoning,
More informationChapter 10 Similarity
Chapter 10 Similarity Def: The ratio of the number a to the number b is the number. A proportion is an equality between ratios. a, b, c, and d are called the first, second, third, and fourth terms. The
More informationNEW YORK GEOMETRY TABLE OF CONTENTS
NEW YORK GEOMETRY TABLE OF CONTENTS CHAPTER 1 POINTS, LINES, & PLANES {G.G.21, G.G.27} TOPIC A: Concepts Relating to Points, Lines, and Planes PART 1: Basic Concepts and Definitions...1 PART 2: Concepts
More informationCourse: Geometry PAP Prosper ISD Course Map Grade Level: Estimated Time Frame 6-7 Block Days. Unit Title
Unit Title Unit 1: Geometric Structure Estimated Time Frame 6-7 Block 1 st 9 weeks Description of What Students will Focus on on the terms and statements that are the basis for geometry. able to use terms
More informationMANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM
COORDINATE Geometry Plotting points on the coordinate plane. Using the Distance Formula: Investigate, and apply the Pythagorean Theorem as it relates to the distance formula. (G.GPE.7, 8.G.B.7, 8.G.B.8)
More information2 nd Semester Final Exam Review
2 nd Semester Final xam Review I. Vocabulary hapter 7 cross products proportion scale factor dilation ratio similar extremes scale similar polygons indirect measurements scale drawing similarity ratio
More informationPerimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh
Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem
More informationGeometry Curriculum Map
Geometry Curriculum Map Unit 1 st Quarter Content/Vocabulary Assessment AZ Standards Addressed Essentials of Geometry 1. What are points, lines, and planes? 1. Identify Points, Lines, and Planes 1. Observation
More informationUnit Number of Days Dates. 1 Angles, Lines and Shapes 14 8/2 8/ Reasoning and Proof with Lines and Angles 14 8/22 9/9
8 th Grade Geometry Curriculum Map Overview 2016-2017 Unit Number of Days Dates 1 Angles, Lines and Shapes 14 8/2 8/19 2 - Reasoning and Proof with Lines and Angles 14 8/22 9/9 3 - Congruence Transformations
More informationWAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ACCELERATED GEOMETRY (June 2014)
UNIT: Chapter 1 Essentials of Geometry UNIT : How do we describe and measure geometric figures? Identify Points, Lines, and Planes (1.1) How do you name geometric figures? Undefined Terms Point Line Plane
More informationDefinition / Postulates / Theorems Checklist
3 undefined terms: point, line, plane Definition / Postulates / Theorems Checklist Section Definition Postulate Theorem 1.2 Space Collinear Non-collinear Coplanar Non-coplanar Intersection 1.3 Segment
More informationKillingly Public Schools. Grades Draft Sept. 2002
Killingly Public Schools Grades 10-12 Draft Sept. 2002 ESSENTIALS OF GEOMETRY Grades 10-12 Language of Plane Geometry CONTENT STANDARD 10-12 EG 1: The student will use the properties of points, lines,
More informationFORMULAS to UNDERSTAND & MEMORIZE
1 of 6 FORMULAS to UNDERSTAND & MEMORIZE Now we come to the part where you need to just bear down and memorize. To make the process a bit simpler, I am providing all of the key info that they re going
More informationWest Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12
West Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12 Unit 1: Basics of Geometry Content Area: Mathematics Course & Grade Level: Basic Geometry, 9 12 Summary and Rationale This unit
More informationHS Geometry Mathematics CC
Course Description This course involves the integration of logical reasoning and spatial visualization skills. It includes a study of deductive proofs and applications from Algebra, an intense study of
More informationIndex COPYRIGHTED MATERIAL. Symbols & Numerics
Symbols & Numerics. (dot) character, point representation, 37 symbol, perpendicular lines, 54 // (double forward slash) symbol, parallel lines, 54, 60 : (colon) character, ratio of quantity representation
More informationShortcuts, Formulas & Tips
& present Shortcuts, Formulas & Tips For MBA, Banking, Civil Services & Other Entrance Examinations Vol. 3: Geometry Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles
More information, Geometry, Quarter 1
2017.18, Geometry, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1.
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More information3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ).
Geometry Kindergarten Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1 Describe objects in the environment using names of shapes,
More informationGeometry. Geometry is one of the most important topics of Quantitative Aptitude section.
Geometry Geometry is one of the most important topics of Quantitative Aptitude section. Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles are always equal. If any
More informationSuggested List of Mathematical Language. Geometry
Suggested List of Mathematical Language Geometry Problem Solving A additive property of equality algorithm apply constraints construct discover explore generalization inductive reasoning parameters reason
More information1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd
Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationCOURSE OBJECTIVES LIST: GEOMETRY
COURSE OBJECTIVES LIST: GEOMETRY Geometry Honors is offered. PREREQUISITES: All skills from Algebra I are assumed. A prerequisites test is given during the first week of class to assess knowledge of these
More information2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? Formula: Area of a Trapezoid. 3 Centroid. 4 Midsegment of a triangle
1 Formula: Area of a Trapezoid 2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? 3 Centroid 4 Midsegment of a triangle 5 Slope formula 6 Point Slope Form of Linear Equation *can
More informationSOL Chapter Due Date
Name: Block: Date: Geometry SOL Review SOL Chapter Due Date G.1 2.2-2.4 G.2 3.1-3.5 G.3 1.3, 4.8, 6.7, 9 G.4 N/A G.5 5.5 G.6 4.1-4.7 G.7 6.1-6.6 G.8 7.1-7.7 G.9 8.2-8.6 G.10 1.6, 8.1 G.11 10.1-10.6, 11.5,
More informationHonors Geometry Pacing Guide Honors Geometry Pacing First Nine Weeks
Unit Topic To recognize points, lines and planes. To be able to recognize and measure segments and angles. To classify angles and name the parts of a degree To recognize collinearity and betweenness of
More informationThe radius for a regular polygon is the same as the radius of the circumscribed circle.
Perimeter and Area The perimeter and area of geometric shapes are basic properties that we need to know. The more complex a shape is, the more complex the process can be in finding its perimeter and area.
More informationCarnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations
Carnegie Learning High School Math Series: Logic and Proofs G.LP.1 Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates,
More informationGeometry Mathematics. Grade(s) 10th - 12th, Duration 1 Year, 1 Credit Required Course
Scope And Sequence Timeframe Unit Instructional Topics 9 Week(s) 9 Week(s) 9 Week(s) Geometric Structure Measurement Similarity Course Overview GENERAL DESCRIPTION: In this course the student will become
More informationHonors Geometry Final Study Guide 2014
Honors Geometry Final Study Guide 2014 1. Find the sum of the measures of the angles of the figure. 2. What is the sum of the angle measures of a 37-gon? 3. Complete this statement: A polygon with all
More informationGEOMETRY. Background Knowledge/Prior Skills. Knows ab = a b. b =
GEOMETRY Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number
More information4. Describe the correlation shown by the scatter plot. 8. Find the distance between the lines with the equations and.
Integrated Math III Summer Review Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help you review topics from previous mathematics courses that are essential to your success
More informationNFC ACADEMY COURSE OVERVIEW
NFC ACADEMY COURSE OVERVIEW Geometry Honors is a full year, high school math course for the student who has successfully completed the prerequisite course, Algebra I. The course focuses on the skills and
More informationTexas High School Geometry
Texas High School Geometry This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet
More informationPractice Test Unit 8. Note: this page will not be available to you for the test. Memorize it!
Geometry Practice Test Unit 8 Name Period: Note: this page will not be available to you for the test. Memorize it! Trigonometric Functions (p. 53 of the Geometry Handbook, version 2.1) SOH CAH TOA sin
More informationAgile Mind CCSS Geometry Scope & Sequence
Geometric structure 1: Using inductive reasoning and conjectures 2: Rigid transformations 3: Transformations and coordinate geometry 8 blocks G-CO.01 (Know precise definitions of angle, circle, perpendicular
More informationMCPS Geometry Pacing Guide Jennifer Mcghee
Units to be covered 1 st Semester: Units to be covered 2 nd Semester: Tools of Geometry; Logic; Constructions; Parallel and Perpendicular Lines; Relationships within Triangles; Similarity of Triangles
More informationOhio s Learning Standards-Extended. Mathematics. Congruence Standards Complexity a Complexity b Complexity c
Ohio s Learning Standards-Extended Mathematics Congruence Standards Complexity a Complexity b Complexity c Most Complex Least Complex Experiment with transformations in the plane G.CO.1 Know precise definitions
More informationGeometry Foundations Planning Document
Geometry Foundations Planning Document Unit 1: Chromatic Numbers Unit Overview A variety of topics allows students to begin the year successfully, review basic fundamentals, develop cooperative learning
More informationThe Research- Driven Solution to Raise the Quality of High School Core Courses. Geometry. Course Outline
The Research- Driven Solution to Raise the Quality of High School Core Courses Course Outline Course Outline Page 2 of 5 0 1 2 3 4 5 ACT Course Standards A. Prerequisites 1. Skills Acquired by Students
More informationGeometry Curriculum Guide Dunmore School District Dunmore, PA
Geometry Dunmore School District Dunmore, PA Geometry Prerequisite: Successful completion Algebra I This course is designed for the student who has successfully completed Algebra I. The course content
More informationGeometry Geometry Grade Grade Grade
Grade Grade Grade 6.G.1 Find the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the
More informationGeometry Foundations Pen Argyl Area High School 2018
Geometry emphasizes the development of logical thinking as it relates to geometric problems. Topics include using the correct language and notations of geometry, developing inductive and deductive reasoning,
More informationPacing Guide. Geometry. Quarter 1
1 Start-Up/ Review ***************** ***** Note: Reteaching from Ready to Go On Quizzes indicate time built in for Intervention lessons/ student mastery of previously taught material. Wk 2 1.1: Understanding
More informationUse throughout the course: for example, Parallel and Perpendicular Lines Proving Lines Parallel. Polygons and Parallelograms Parallelograms
Geometry Correlated to the Texas Essential Knowledge and Skills TEKS Units Lessons G.1 Mathematical Process Standards The student uses mathematical processes to acquire and demonstrate mathematical understanding.
More informationCourse: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days
Geometry Curriculum Chambersburg Area School District Course Map Timeline 2016 Units *Note: unit numbers are for reference only and do not indicate the order in which concepts need to be taught Suggested
More informationMADISON ACADEMY GEOMETRY PACING GUIDE
MADISON ACADEMY GEOMETRY PACING GUIDE 2018-2019 Standards (ACT included) ALCOS#1 Know the precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined
More informationSOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal)
1 SOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal) 1. Basic Terms and Definitions: a) Line-segment: A part of a line with two end points is called a line-segment. b) Ray: A part
More informationAgile Mind Geometry Scope and Sequence, Common Core State Standards for Mathematics
Students began their study of geometric concepts in middle school mathematics. They studied area, surface area, and volume and informally investigated lines, angles, and triangles. Students in middle school
More informationMathematics Standards for High School Geometry
Mathematics Standards for High School Geometry Geometry is a course required for graduation and course is aligned with the College and Career Ready Standards for Mathematics in High School. Throughout
More informationHustle Geometry SOLUTIONS MAΘ National Convention 2018 Answers:
Hustle Geometry SOLUTIONS MAΘ National Convention 08 Answers:. 50.. 4. 8 4. 880 5. 6. 6 7 7. 800π 8. 6 9. 8 0. 58. 5.. 69 4. 0 5. 57 6. 66 7. 46 8. 6 9. 0.. 75. 00. 80 4. 8 5 5. 7 8 6+6 + or. Hustle Geometry
More informationNorthern York County School District Curriculum
Course Name Keystone Geometry (1.03 / 1.06 / 1.10) Grade Level Grade 10 Northern York County School District Curriculum Module Instructional Procedures Module 1: Geometric Properties and Reasoning Course
More informationTriangles. Leg = s. Hypotenuse = s 2
Honors Geometry Second Semester Final Review This review is designed to give the student a BASIC outline of what needs to be reviewed for the second semester final exam in Honors Geometry. It is up to
More informationGeometry Vocabulary. Name Class
Geometry Vocabulary Name Class Definition/Description Symbol/Sketch 1 point An exact location in space. In two dimensions, an ordered pair specifies a point in a coordinate plane: (x,y) 2 line 3a line
More informationAldine ISD Benchmark Targets /Geometry SUMMER 2004
ASSURANCES: By the end of Geometry, the student will be able to: 1. Use properties of triangles and quadrilaterals to solve problems. 2. Identify, classify, and draw two and three-dimensional objects (prisms,
More informationHigh School Geometry
High School Geometry This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationGeometry Honors Curriculum Guide Dunmore School District Dunmore, PA
Geometry Honors Dunmore School District Dunmore, PA Geometry Honors Prerequisite: Successful Completion of Algebra I Honors K This course is designed for the student who has successfully completed Algebra
More informationFLORIDA GEOMETRY EOC TOOLKIT
FLORIDA GEOMETRY EOC TOOLKIT CORRELATION Correlated to the Geometry End-of-Course Benchmarks For more information, go to etacuisenaire.com\florida 78228IS ISBN 978-0-7406-9565-0 MA.912.D.6.2 Find the converse,
More informationAssignment List. Chapter 1 Essentials of Geometry. Chapter 2 Reasoning and Proof. Chapter 3 Parallel and Perpendicular Lines
Geometry Assignment List Chapter 1 Essentials of Geometry 1.1 Identify Points, Lines, and Planes 5 #1, 4-38 even, 44-58 even 27 1.2 Use Segments and Congruence 12 #4-36 even, 37-45 all 26 1.3 Use Midpoint
More informationSequence of Geometry Modules Aligned with the Standards
Sequence of Geometry Modules Aligned with the Standards Module 1: Congruence, Proof, and Constructions Module 2: Similarity, Proof, and Trigonometry Module 3: Extending to Three Dimensions Module 4: Connecting
More informationGeometry. Instructional Activities:
GEOMETRY Instructional Activities: Geometry Assessment: A. Direct Instruction A. Quizzes B. Cooperative Learning B. Skill Reviews C. Technology Integration C. Test Prep Questions D. Study Guides D. Chapter
More informationMaryland Geometry UNIT 1: FOUNDATIONS OF GEOMETRY. Core
Core Geometry builds upon students' command of geometric relationships and formulating mathematical arguments. Students learn through discovery and application, developing the skills they need to break
More informationGeometry. Geometry. Domain Cluster Standard. Congruence (G CO)
Domain Cluster Standard 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
More informationFONTANA UNIFIED SCHOOL DISTRICT Glencoe Geometry Quarter 1 Standards and Objectives Pacing Map
Glencoe Geometry Quarter 1 1 August 9-13 2 August 16-20 *1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
More informationExample Items. Geometry
Example Items Geometry Geometry Example Items are a representative set of items for the ACP. Teachers may use this set of items along with the test blueprint as guides to prepare students for the ACP.
More informationRussell County Pacing Guide
August Experiment with transformations in the plane. 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance
More informationMadison County Schools Suggested Geometry Pacing Guide,
Madison County Schools Suggested Geometry Pacing Guide, 2016 2017 Domain Abbreviation Congruence G-CO Similarity, Right Triangles, and Trigonometry G-SRT Modeling with Geometry *G-MG Geometric Measurement
More informationGeometry. Cluster: Experiment with transformations in the plane. G.CO.1 G.CO.2. Common Core Institute
Geometry Cluster: Experiment with transformations in the plane. G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of
More informationGeometry 10 and 11 Notes
Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into
More informationGeometry. (F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is (A) apply mathematics to problems arising in everyday life,
More informationCommon Core Cluster. Experiment with transformations in the plane. Unpacking What does this standard mean that a student will know and be able to do?
Congruence G.CO Experiment with transformations in the plane. G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,
More informationThe Research- Driven Solution to Raise the Quality of High School Core Courses. Geometry. Instructional Units Plan
The Research- Driven Solution to Raise the Quality of High School Core Courses Instructional Units Plan Instructional Units Plan This set of plans presents the topics and selected for ACT s rigorous course.
More information10.6 Area and Perimeter of Regular Polygons
10.6. Area and Perimeter of Regular Polygons www.ck12.org 10.6 Area and Perimeter of Regular Polygons Learning Objectives Calculate the area and perimeter of a regular polygon. Review Queue 1. What is
More informationGeometry. AIR Study Guide
Geometry AIR Study Guide Table of Contents Topic Slide Formulas 3 5 Angles 6 Lines and Slope 7 Transformations 8 Constructions 9 10 Triangles 11 Congruency and Similarity 12 Right Triangles Only 13 Other
More informationGanado Unified School District Geometry
Ganado Unified School District Geometry PACING Guide SY 2016-2017 Timeline & Resources 1st Quarter Unit 1 AZ & ELA Standards Essential Question Learning Goal Vocabulary CC.9-12.G.CO. Transformations and
More informationCommon Core Specifications for Geometry
1 Common Core Specifications for Geometry Examples of how to read the red references: Congruence (G-Co) 2-03 indicates this spec is implemented in Unit 3, Lesson 2. IDT_C indicates that this spec is implemented
More informationAchievement Level Descriptors Geometry
Achievement Level Descriptors Geometry ALD Stard Level 2 Level 3 Level 4 Level 5 Policy MAFS Students at this level demonstrate a below satisfactory level of success with the challenging Students at this
More informationHigh School Geometry
High School Geometry This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationGeometry/Pre AP Geometry Common Core Standards
1st Nine Weeks Transformations Transformations *Rotations *Dilation (of figures and lines) *Translation *Flip G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle,
More informationCURRICULUM GUIDE. Honors Geometry
CURRICULUM GUIDE Honors Geometry This level of Geometry is approached at an accelerated pace. Topics of postulates, theorems and proofs are discussed both traditionally and with a discovery approach. The
More informationMathematics Scope & Sequence Geometry
Mathematics Scope & Sequence 2016-17 Geometry Revised: June 21, 2016 First Grading Period (24 ) Readiness Standard(s) G.5A investigate patterns to make conjectures about geometric relationships, including
More informationTest #1: Chapters 1, 2, 3 Test #2: Chapters 4, 7, 9 Test #3: Chapters 5, 6, 8 Test #4: Chapters 10, 11, 12
Progress Assessments When the standards in each grouping are taught completely the students should take the assessment. Each assessment should be given within 3 days of completing the assigned chapters.
More informationStandards to Topics. Common Core State Standards 2010 Geometry
Standards to Topics G-CO.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
More informationK-12 Geometry Standards
Geometry K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1. Describe objects in the environment using names of shapes, and describe
More informationGEOMETRY CP1: Final Review Homework Packet
GEOMETRY CP1: Final Review Homework Packet Similarity Pythagorean Theorem & Right Triangles Area Surface Area & Volume Trigonometry Circles Name: Geometry CP1 Final Exam Information & Advice General Information:
More informationGeometry Mathematics. Grade(s) 9th - 12th, Duration 1 Year, 1 Credit Required Course
Course Description will provide a careful development of both inductive and deductive reasoning. While emphasizing the formal geometric topics of points, lines, planes, congruency, similarity, and characteristics
More informationT103 Final Review Sheet. Central Angles. Inductive Proof. Transversal. Rectangle
T103 Final Review Sheet Know the following definitions and their notations: Point Hexa- Space Hepta- Line Octa- Plane Nona- Collinear Deca- Coplanar Dodeca- Intersect Icosa- Point of Intersection Interior
More informationPearson Mathematics Geometry
A Correlation of Pearson Mathematics Geometry Indiana 2017 To the INDIANA ACADEMIC STANDARDS Mathematics (2014) Geometry The following shows where all of the standards that are part of the Indiana Mathematics
More informationGeometry First Semester Practice Final (cont)
49. Determine the width of the river, AE, if A. 6.6 yards. 10 yards C. 12.8 yards D. 15 yards Geometry First Semester Practice Final (cont) 50. In the similar triangles shown below, what is the value of
More informationPearson Mathematics Geometry Common Core 2015
A Correlation of Pearson Mathematics Geometry Common Core 2015 to the Common Core State Standards for Bid Category 13-040-10 A Correlation of Pearson, Common Core Pearson Geometry Congruence G-CO Experiment
More information