HONORS GEOMETRY CHAPTER 1 WORKBOOK

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2 Honors Geometry Skills Review Worksheet For numbers 1 3, solve each equation. 1. 8x 2 = 9 + 7x = 4( 6x 3) 3. 5(1 5x) + 5( 8x 2) = 4x 8x For numbers 4 6, simplify each expression by multiplying. 4. 2x( 2x 3) 5. (8p 2)(6p + 2) 6. (n 2 + 6n 4)(2n 4) For numbers 7 9, factor each expression. 7. b 2 + 8b b b n 2 + 5n + 2 For numbers 10 14, solve each equation n = (k + 1)(k 5) = n 2 + 7n + 15 = n 2 10n + 22 = m 2 7m 13 = 10 For numbers 15 18, simplify each radical

3 Honors Geometry Algebra Skills Practice I. Solving Linear Equations 1. 2x + 5 = x + 5 = (x 3) = x 32 = (2x + 5) 3x = x 4(x 4) + 4 = 13 II. Solving Systems of Equations by Elimination. 7. 2x 7y 3 4x 2y x y 39 x y x 4y 7 15 x 12y x 3y 39 6x 12y 19 III. Solving Systems of Equations by Substitution 11. x 6y 2 5x 30y x 2y 6 5x 4y x 3y 8 9x 3y x 5y x 30y 81 2

4 IV. Simplifying Radicals V. Solving Quadratic Equations by the Quadratic Formula 24. x 2 x = x = 6x 26. 4x 2 = 4x x 2 3x = 7 VI. Solving Quadratic Equations by Factoring (when a = 1) 28. x 2 2x 35 = x 2 10x 24 = x 2 9x = 2x x = x 2 3

5 VII. Solving Quadratic Equations by Factoring (when a 1) 32. 2x 2 + x 3 = x 35 = 4x x + 21 = 14x x x + 36 = 0 VIII. Solving Special Cases of Quadratic Equations 36. x 2 3 = x = 19, x = 40x x = x = x x 2 6x = 11x IX. Solving Radical Equations and Proportions 42. 3x x y 1 y 3 y 45. x x 8 2x 6 15

6 Common Core State Standards G. CO. 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 around a circular arc. Learning Targets 1. Students will be able to identify and model points, lines, and planes. 2. Students will be able to identify intersecting lines and planes. Section 1.1 Notes: Points, Lines, and Planes Vocabulary Word Definition Picture No Picture Necessary. Undefined terms Provide Examples: Point Named by : Line Named by : Plane Named by : Collinear Points Coplanar Points Example 1: a) Use the figure to name a line containing point K. b) Use the figure to name a plane containing point L.

7 Example 2: Name the geometric shape modeled by a patio. Example 4: Create a real-life example for a plane. Example 3: Name the geometric shape modeled by a button on a table. Example 5: Create a real-life example for a line. Vocabulary Definition Picture Intersection ***Two or more geometric figures intersect if they have one or more points in common. Example 6: = b) = Example 7: Draw and label a figure for the following situation. Plane R contains lines AB and DE, which intersect at point P. Add point C on plane R so that it is not collinear with AB or DE. Example 8: Draw and label a figure for the following situation. QR on a coordinate plane contains Q( 2, 4) and R(4, 4). Add point T so that T is collinear with these points. Vocabulary Definition Examples Defined Terms Space

8 Example 9: a) How many planes appear in this figure? b) Name three points that are collinear. c) Are points A, B, C, and D coplanar? Explain. d) At what point do DB and CA intersect? Honors Geometry Pages 8 11: Numbers 15, 18, 36, 44, 46, 58, Textbook Homework

10 Common Core State Standards G.CO.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 around a circular arc. G. CO. 12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc. ) Learning Targets 1. Students will measure segments. 2. Students will be able to calculate with measures. Section 1.2 Notes: Linear Measure Vocabulary Definition Picture Line Segment Named by : Example 1: a) Find the length of AB using the ruler. b ) Find the length of AB using the ruler. Vocabulary Definition Picture Betweeness of Points Example 2: Find XZ. Assume that the figure is not drawn to scale. Example 3: Find LM. Assume that the figure is not drawn to scale.

11 Example 4: Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x 3. Draw a picture here! Vocabulary Definition Picture Congruent Segments Named by : What symbol is used to indicate congruence? Example 5: The perimeter of (the distance around) ABCD is 66, and is twice as long as How long is Given:, D C A B

Linear Measure and Precision Extra Problems Find the length and precision of each object: 1. mab 2. Length of pencil = 3. C mcd D 4. mef 5. What does AB = 2.3cm mean? 6.

12 Linear Measure and Precision Extra Problems Find the length and precision of each object: 1. mab 2. Length of pencil = 3. C mcd D 4. mef 5. What does AB = 2.3cm mean? 6. What does mcd 1 1 in 4 mean? 7. If CA BO, and mca 0.6cm, find BO If TI ME, and ME = 1 in, find mti. 8 Find the measure of each segment: 9. AC = 10. ST = 11. WX =

13 Create a diagram for each problem, solve for the missing values. 19. Point B is between points A and C. If AC=32, AB = 17, and BC = 3m, draw a diagram labeling the value for each segment: 20. Point B is between points A and C. If AC=7b+13, AB = 25, and BC = 3b, draw a diagram labeling the value for each segment: 21. Point B is between points A and C. If AC=65, AB = 6c - 8, and BC = 3c+1, draw a diagram labeling the value for each segment: Equation to solve for m: Equation to solve for b: Equation to solve for :c m = BC = b = AC = BC = c = AB = BC = 22. Point S is between points R and T. If RS =16, ST = 2x, and RT = 5x+10, draw a diagram labeling the value for each segment: 23. Point S is between points R and T. If RS=3y+1, ST=2y, and RT = 21, draw a diagram labeling the value for each segment: 24. Point S is between points R and T. If RS =4y-1, ST = 2y-1, RT = 5y, draw a diagram labeling the value for each segment: Equation to solve for x: Equation to solve for y: Equation to solve for y: x = ST = RT = y = RS = ST = y = RS = ST = RT = Use the figure to determine whether each pair of segments is congruent. Fill the space with the appropriate symbol (, ), and if appropriate draw tick marks on the diagram. 25. AB CD 26. XY YZ Hint: solve for x first 27. NP MP

14 Honors Geometry Page 19 & 20: 20, 26, 32, 39, Textbook Homework

16 Common Core State Standards G.CO.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 around a circular arc. G. CO. 12 Make formal geometric constructions with a variety of tools and methods. Student Learning Target 1. Students will be able to find the distance between two points. 2. Students will find the midpoint of a segment. Section 1.3 Notes: Distance and Midpoints Vocabulary Definition Picture Distance Distance Formula (on Number Line) Example 1: Use the number line to find QR. Vocabulary Definition Picture Distance Formula (in Coordinate Plane) Example 2: Find the distance between E( 4, 1) and F(3, 1). Vocabulary Definition Picture Midpoint Midpoint Formula (on Number Line)

17 Example 3: a) Given:, Find the value of x. b) Is Q the midpoint of Vocabulary Definition Picture Midpoint Formula (in Coordinate Plane) Example 4: Find the coordinates of M, the midpoint of GH, for G(8, 6), and H( 14, 12). Example 5: Find the coordinates of D if E( 6, 4) is the midpoint of DF and F has coordinates ( 5, 3). Vocabulary Definition Picture Segment bisector

18 Honors Geometry Pages 31 34: Numbers 12, 31, 32, 44, 52, 66, Textbook Homework

20 Common Core State Standards G.CO.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 around a circular arc. G. CO. 12 Make formal geometric constructions with a variety of tools and methods. Student Learning Target 1. Students will be able to measure and classify angles. 2. Students will be able to identify and use congruent angles and the bisector of an angle. Section 1.4 Notes: Angle Measure Vocabulary Definition Picture Ray Named by: Opposite Rays Angle Named By : Sides Vertex Interior of the Angle Exterior of the Angle Example 1: Use the diagram below. a) Name all angles that have B as a vertex. b) Name the sides of 5. c) Write another name for 6.

21 Classifying Angles Vocabulary Definition Picture Right Angle Symbol that indicates a 90 degree angle : Acute Angle Obtuse Angle Congruent Angles Example 2: Symbol that indicates congruent angles: a) Measure TYV and classify it as right, acute, or obtuse. b) Measure WYT and classify it as right, acute, or obtuse. c) Measure TYU and classify it as right, acute, or obtuse. Example 3: and have the same measure. If ( ) and ( ) is a straight angle? C A B D Example 4: Given: is a straight angle. is a right angle. ( ( Solve for x and y. X T R S

22 Vocabulary Definition Picture Angle bisector Example 5: Given: ( ( ( Has been trisected? C A B Example 6: RT bisects QRS. Example 7: KM bisects JKL. Given that m QRS= 60, what are The measures of the two congruent the measures of QRT & TRS? angles are 2x 7 x b g and b4 41g. Find the measures of JKM and MKL. Degrees, Minutes, and Seconds Degree measure is divided into smaller portions, minutes and seconds. One degree is equivalent to equivalent to 60 seconds. minutes and one minute is 1 = 60ʹ 1ʹ = 60ʹʹ Example 7: 5 a) Convert121 8 to degrees, minutes, and seconds. b) Convert to degrees and minutes. Example 8: a) Change to degrees. b) Change to degrees.

23 Clock Problems Example 9: Find the angle of the hands of the clock at: a) 9:40 b) 3:50 c) 7:25 d) 11:20

24 Honors Geometry Clock Problems Worksheet 1. 8: : : : Convert 46 into degrees, minutes and seconds Your latitude is 13 40ʹ20ʹʹ. In order to program these coordinates into your GPS, you must convert the measurement to degrees only. [Hint: you are working backwards in the previous example.] 7. Two angles are complementary (they add to 90 ). If one angle has a measure of 36 14ʹ25ʹʹ, find the measure of the second angle (the complement).

25 8. The straight angle is divided by rays RK and RJ in the ratio of 6:4:2. Find the m JRT. K J M R T 9. RQP is a right angle m RQS = (2x + 19) m SQP = (7x 10) Find the value of x. P S Q R Honors Geometry Pages 41 43: Numbers 28, 41, 44, Textbook Homework

26 Common Core State Standards G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Student Learning Targets 1. Students will be able to identify and use special pairs of angles. 2. Students will be able to identify perpendicular lines. Section 1.5 Notes: Angle Relationships Vocabulary Definition Picture Non-examples Adjacent Angles Linear Pair Vertical Angles Special Characteristic - Example 1: a) Name an angle pair that satisfies the condition two angles that form a linear pair. b) Name an angle pair that satisfies the condition two right vertical angles. Angle Pair Relationships Vocabulary Definition Picture Complementary Angles Supplementary Angles Example 2: Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle. Example 3: Find the measures of two complementary angles if the measures of the larger angle is 12 more than twice the measure of the smaller angle.

27 Vocabulary Definition Picture Perpendicular Lines 1. Characteristics of Perpendicular Lines Example 4: Find x and y so that KO and HM are perpendicular. CAN be Assumed Diagram CANNOT be Assumed Example 5: Determine whether the following statement can be justified from the figure below. Explain. a) m VYT = 90 b) TYW and TYU are supplementary. c) VYW and TYS are adjacent angles.

28 Example 6: is a right angle. The ratio of the measures of and is 3 to 2. Find. (Hint: Let and ) A D B C Honors Geometry Pages 51 & 52: Numbers 11, 24, 26, 28, 34, 36, 38, Textbook Homework

30 Common Core State Standards G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. Student Learning Targets 1. Students will be able to identify and name polygons. 2. Students will be able to find the perimeter, circumference, and area of two-dimensional figures. Section 1.6 Notes: Two-Dimensional Figures Vocabulary Definition Picture Polygon Vertex of the Polygon Examples of Polygons Examples of Not Polygons Example 1: Determine if the following are polygons. If no, explain why. Vocabulary Definition Picture Concave Convex N-gon

31 Number of Sides 3 Polygon N n-gon Vocabulary Definition Picture Equilateral Polygon Equiangular Polygon Regular Polygon Example 2: Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Provide a justification in your decision. a) b) Justification: Justification:

Vocabulary Definition Picture Perimeter Circumference Area Triangle Square Rectangle Circle Perimeter: Perimeter: Perimeter: Perimeter: Area: Area: Area: Area: Example 3: a) Find the perimeter and

32 Vocabulary Definition Picture Perimeter Circumference Area Triangle Square Rectangle Circle Perimeter: Perimeter: Perimeter: Perimeter: Area: Area: Area: Area: Example 3: a) Find the perimeter and area of the figure. b) Find the circumference and area of the figure. Example 4: Multiple Choice Terri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these shapes has a perimeter or circumference that would use most or all of the tape? a) square with side length of 5 feet b) circle with the radius of 3 feet c) right triangle with each leg length of 6 feet d) rectangle with a length of 8 feet and a width of 3 feet

Your budget limits you to only enough stone to cover 104 square yards. How wide should the border be?

33 Example 5: Find the perimeter and area of the figure on the right. Example 6: You are putting a stone border along two sides of a rectangular Japanese garden that measures 8 yards by 14 yards. Your budget limits you to only enough stone to cover 104 square yards. How wide should the border be? 14 8 Perimeter and Area on the Coordinate Plane Example 7: Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, 4), D( 3, 4), and E( 3, 1). Example 8: Find the perimeter of quadrilateral WXYZ with W(2, 4), X( 3, 3), Y( 1, 0), and Z(3, 1).

34 Honors Geometry Pages 62 & 63: Numbers 26, 32, 45, Textbook Homework

Chapter 1 Here are the rules of the game.

(no measuring) and a compass to construct

You ve got this!! Note: Visit http://www.

36 Chapter 1 Here are the rules of the game. You are only allowed to use a straightedge (no measuring) and a compass to construct the following. See if you can win the game. You ve got this!! Note: Visit for additional help. 1) Copy a Segment: Practice YOU TRY 2) Bisect a Segment: Practice YOU TRY

37 3) Copy an Angle: Practice YOU TRY 4) Bisect an Angle: YOU TRY

38 5) Perpendiculars: a) Construct a line perpendicular to line l and passing through point P on l. Practice YOU TRY b) Construct a line perpendicular to line k and passing through point P not on k. Practice YOU TRY

39 Reflective Questions: 1) How specifically does the compass help you? (Hint: Think about what it allows you to do without actually measuring distance) 2) What do you think is the purpose of constructing something rather than measuring it out (this is open-ended; I want to know what you think)? 3) Did you find this activity helpful in understanding vocabulary (i.e. bisector, perpendicular, etc.)? Explain. Be honest. Practice (try without looking at the steps) 1) 2) 3) 4) 5a) 5b)

Geometry. Chapter 1 Points, Lines, Planes, and Angles

Geometry. Chapter 1 Points, Lines, Planes, and Angles Geometry Chapter 1 Points, Lines, Planes, and Angles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** Algebraic Equations Review Keystone Vocabulary