Geometry Honors Summer Assignment 2018/19 School Year

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1 Geometry Honors Summer Assignment 2018/19 School Year This summer assignment is review of all material that is important to know for the Geometry Honors course. Each topic is broken down into categories as they apply to the Geometry Honors Curriculum. Topic 1: Ratio and Proportion Topic 2: Problems involving Area, Surface Area, and Volume Topic 3: Congruency Topic 4: Factoring Topic 5: Equations of Lines Topic 1: Ratio and Proportion: (7.RP.1) Category 1: Solving ratios involving factoring Key things to remember: A ratio is a comparison. Ratios can be written with a colon such as 1:3, or as a fraction like, 1. You will see ratios presented both ways in Geometry. 3 Understanding how to set up a proportion and solve is a key concept. Ex: x+6 x = 3 2 Ex: x = 12 3x Ex: x+2 4 = x x 3 Ex: x 1 2 = 2 x+2 Ex: b+1 b 1 = 5 6 Ex: x+3 2x = x x+2

2 Category 2: Using ratio and proportion to find lengths, angles, and areas. Key things to remember: Always set up an equation or proportion to solve for missing length. Reread question in order to solve for the appropriate answer. When the ratio is given using a colon, attach an x to each, and add to solve the equation. Key vocabulary: Perimeter: The distance around an object. Found by adding all sides Area: The space inside of a 2D object. Ex: The angles of a triangle are in a ratio of 2:3:4. Find the measure of each angle. 2x + 3x + 4x = 180 9x = 180 X = 20 Therefore each angle is 40, 60, 80 respectively. Ex: The angles of quadrilateral are in a ratio of 2:3:6:7. Find the measure of each angle. Ex: In a rectangle the adjacent sides are in a 2:3 ratio. If the perimeter is 45, find the area. Ex: The ratio of the adjacent sides of a rectangle is 2:5, if the perimeter 63, find the length of each side of the rectangle.

3 Solving Problems Involving Area, S.A. and Volume: (7.G.3, 7.G.4, 7.G.5, 7.G.6, 8.G.9) Category 1: Know all area formulas: Rectangle: (b)(h) Triangle: (b)(h) 2 Rhombus: d 1 d 2 2 Square: s 2 Trapezoid: ( b 1+ b 2 )(h) 2 Circle: r 2 π 5.

4 6. Category 2: Geometry terms and solving questions containing the vocabulary. Define the following: Supplementary: Complementary: Linear Pair: Vertical Angles: Key thing to remember: Questions will include the previous vocabulary. It is important to know the definitions in order to be able to set up equations and solve accordingly. Ex: Using the diagram below, which of the following angles are a linear pair? D E A B C (1) <ABD & <EBC (3) <ABD & <DBC (2) <EBC & <DBE (4) <ABC & <DBC

5 Ex: Name an angle complementary to <COD. B C A O D E (1) <COB (3) <COE (2) <AOE (4) <COA Ex: Two angles are complementary. One angle measures 15 less than twice the other. Find the measure of each angle. Ex: AB and CD intersect at E. If <CEA is 3x, and <BED is 5x 64, find <AED.

6 Category 3: Volume and Surface Area of 3D Shapes Define the following: Volume: Surface Area: Prism: Cube: Cone: Cylinder: Sphere: Know the following formulas: Volume: Prism: (B)(h) {B represents area of the base and h represents height of the prism} Cube: S 3 {S is the length of a side} Cylinder: (B)(h) {B = r 2 π and h is the height of the cylinder} Cone: (B)(h) 3 {B = r 2 π and h is the height of the cone} Sphere: 4 3 r3 π {r is the radius of the sphere}

7 Ex: Ex: Ex:

8 Ex: A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is empty? Ex: Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere weighs.075 pound per cubic inch. If the sphere's radius is 4 inches, what is the weight of the sphere, to the nearest pound? Congruency: (8.G.1, 8.G.2, 8.G.3, 8.G.4, 8.G.5, 8.G.6, 8.G.7 Category 1: Parallel Lines cut by a Transversal Define the following: Parallel Lines: Transversal: Alternate Interior Angles: Corresponding Angles: Same Side Interior Angles:

9 Ex: A 1 2 B C 7 8 D 1. Angles 3 and 6 are known as. 2. Angles 5 and 8 are known as. 3. Angles 3 and 7 are known as. 4. Angles 2 and 8 are known as. 5. Angles 1 and 2 are known as a. 6. If m <8 = 43 degrees, fill in the measure of each of the missing angles: <1 = <2= <3= <4= <5= <6=

10 Ex: If parallel lines are cut by a transversal and the two same side interior angles are represented by 5x 12 and 2x + 3, then find the measure of each angle. Ex: In the figure below of two parallel lines cut by a transversal; list the pairs of corresponding angles Category 2: Triangle Properties Key things to remember for this category: degrees in a triangle, the different types of triangles and their properties to set up equations to solve, exterior angle theorem of triangles to set up equations and solve, side inequality theorem. The sum of the angles of a triangle equal. Types of Triangles: Acute Triangle: Picture:

11 Obtuse Triangle: Picture: Right Triangle: Picture: Isosceles Triangle: Picture: Equilateral Triangle: Picture: Scalene Triangle: Picture: Ex: In a triangle, two of the angles measure 55º and 35º. This triangle can be classified as:

12 Ex: Can an obtuse triangle have two obtuse angles? Explain your answer in writing. Ex: In a triangle, the second angle of a triangle is 25º more than the first angle. The third angle is 10º less than 3 times the first angle. What type of triangle is this? Side Inequality Theorem: If you are given two sides of a triangle, the third side will be a number between their difference and their sum. Ex: Two sides of a triangle are 5 and 8, what could be the third side? 8 5 = = 13 Therefore: The third side could be equal to 4,5,6,7,8,9,10,11,12 Ex: If the lengths of the sides of a triangle are 3 and 11, what could be the length of the third side? Ex: If the lengths of the sides of a triangle are 6 and 14, what could be the length of the third side?

13 Category 3: Pythagorean Theorem: Key things to know: How to label the parts of a right triangle, the formula for Pythagorean theorem, and how to substitute in correctly to solve for missing sides of a right triangle. Putting answers in simplest radical form when necessary. To put into simplest radical form always find the largest perfect square that goes into the number Ex: Simplify: 98 Simplify: 72 Simplify: 204 Pythagorean Theorem: a 2 + b 2 = c 2 a and b are the measures of the legs of the right triangle, c is the measure of the hypotenuse of the right triangle. Leg Hypotenuse Leg

14 Ex: If the legs of a right triangle measure 3 and 4, find the length of the hypotenuse. a 2 + b 2 = c = x = x 2 25 = x 2 5 = x Ex: If the hypotenuse measures 13 and a leg measures 12, find the length of the other leg. a 2 + b 2 = c x 2 = x 2 = 169 x 2 = 25 x = 5 Ex: If the measure of the hypotenuse of a right triangle is 17 and the measure of one of the legs is 8, find the measure of the other leg. Ex: If the measure of the legs of a right triangle are 8 and 15, find the measure of the hypotenuse. Ex: If the two legs of a right triangle are 3 and 6, what is the length of the hypotenuse in simplest radical form?

15 Category 4: Basic Transformations Key things to know: There are 4 transformations: reflection, rotation, translation, dilation Define: Reflection: Rotation: Translation: Dilation: Ex:. J(2,-1), A(-2,-2), and R (-4,1). Reflect triangle JAR over the x axis. Ex: If A (2, 5) has a transformation of T(-3, 2), what are the coordinates of point A 1?

16 Ex:. P(2, -1), A(-2,-2), and M (-4,1). Rotate triangle PAM 270 counterclockwise about the origin. Ex: If D(-4, 6) E(3, -2) is dilated by a factor of 3, what are the coordinates of D 1 and E 1? Ex:. J(2,-1), A(-2,-2), and R (-4,1). Reflect triangle JAR over the y axis.

17 Topic 4: Factoring (A-REI) Key things to know for this topic are factoring for any type of trinomial, double distribution for biniomials, factoring by completing the square, factoring by grouping. Multiplying Binomials: Ex: (3x + 1) 2 Ex: (c + 5) (c 4) Ex: (w 2) 2 Factoring Trinomials: Ex: x 2 x 6 Ex: x 2 + 7x + 12 Ex: x 2 + 2x - 8 Factoring by Grouping: Ex: 4x 2 7x 15 Ex: 6x 2 + 5x 6 Ex: 3x 2 + 7x 20

18 Factoring by Completing the Square Ex: x x + 40 = 0 Ex: x 2 10x + 7 = 0 Ex: x 2 6x 16 = 0 Topic 5: Equations of Lines (F-IF.4, F-IF.7) The key concepts from this topic are knowing how to find the slope of a line algebraically, writing the equation of a line, understanding what each part of the equation represents in order to solve and find line equations. Define: Slope: y-intercept: Equation of a Line: Slope Formula: (y 2 y 1 ) (x 2 x 1 ) Ex: Given M(2, -5) and N(-3, 2), find the slope of the line containing these points.

19 Ex: Find the slope of RS if R (-4, 6) and S(1, -2) have the given coordinates. Ex: In the given equation, 2x y = -5, what is the slope and y-intercept? Ex: Does the point (-1, 3) line on the equation y = 3x + 5? Only an algebraic answer is acceptable. Ex: Write the equation of a line that contains, and has a slope of -4. Ex: Find the slope and the y-intercept of the following line if 3x 2y = 10. Ex: Does the point (5, -3) lie on the equation 10 5y = x, only an algebraic solution is acceptable.

Moore 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