Unit 1 Geometry Basics Homework 5 Angle Relationships Answer Key
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Name: ___________________________ Block: ____ Ch 1: The Essentials of Geometry PRACTICE PROBLEMS Assignment Score Learning Target(s) Notes What am I confident about? Where do I need to spend more time? Am I weak on a prerequisite skill? What am I going to do if I am weak? 1.1 18 1.2 20 1.3 22 1.1-1.3 Review 28 1.4 30 1.5 24 Ch Review 20 Learning Targets: Name and sketch geometric figures Use segment postulates to identify congruent segments Find lengths of segments in the coordinate plane Name, measure, and classify angles Use special angle relationships to find angle measures Unit 2 Syllabus: Ch 1 Essentials of Geometry Block Date Topic Homework 7 9/22 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence Wkst: 1.1 Definitions and 1.2 Segment Addition Postulate 8 9/24 1.3 Use Midpoint and Distance Formulas Wkst: 1.3 Midpoint and Distance 9 9/26 Review Day Wkst: 1.1-1.3 Review 10 9/30 Quiz 1.1-1.3 Spiral Review 11 10/2 1.4 Measure and Classify Angles Wkst: 1.4 Angle Measurement 12 10/4 1.5 Describe Angle Pair Relationships Wkst: 1.5 Angle Relationships 13 10/6 Review Day Wkst: Chapter 1 Review 14 10/8 Chapter 1 Test Spiral Review ***Syllabus subject to change due to weather, pep rallies, illness, etc Need Help? Mrs. Prusak are available in the morning. Email her to set up a time! Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L409. Need to make up a test/quiz? Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons. 2 HW: 1.1 Points, Lines, and Planes In Exercises 1–6, use the diagram. 1. Are points J, K, and L collinear or coplanar? 2. Are points J, K, and M collinear or coplanar? 3. Name the intersection of and . 4. Name the intersection of and plane KMN. 5. Name the intersection of plane R and plane S. 6. Name three pairs of opposite rays. Use Diagram to left to answer questions 7-9 7. Name 12 different rays. 8. Name 2 pairs of opposite rays. 9. Name 2 lines that intersect at point Z. 3 K L P Q P Q 1 8 Using the appropriate labels sketch the following relationships. 13. AB intersects CD 14. X is not on AB 15. Points L, M, and N are collinear 16. Points L, M, and N are noncollinear 17. RS intersects plane Q at P 18. Plane Q intersects plane R at EF 4 HW: 1.2 Use Segments and Congruence 5 1 9 Find the indicated length. 6 HW: 1.3 Midpoint and Distance 7 2 2 Refer to the coordinate plane below to find the following. 16. The coordinates of A. 17. The coordinates of B. 18. The coordinates of C. 19. The coordinates of D. 20. The coordinates of E. 21. The distance from D to C. 22. The distance from E to A. 8 HW: Review 1.1-1.3 1. In the diagram of collinear points, , and .GK HJ GH HI IJ 24 10 Find the length of each segment. a. HI=_____ b. IJ=_____ c. GH=_____ d. JK=_____ e. IG=_____ f. IK=_____ Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. 17. HJ x JK x KH x 2 2 8 9 5 1 18. HJ x JK x KH 2 4 3 1 22 19. Determine if the following segments are congruent. Write a congruence statement if they are. Show all work to support and explain your answer. AB : A(1,-3), B(0,5) CD : C(1,1), D(-3,4) 9 G KH I J 2 8 20. Let E be a segment bisector of FG . Given FE= 8w-8, EG = 4w-4. Find the value of w. 21. The midpoint of AB is M(-6, 2). If the coordinates of point A are (4, 2), find the coordinates of the other endpoint, B. Find the length of the segments with the given endpoints. 22. 2, 4 4,2A B 23. 3,5 1,1A B Find the midpoint of the segment with the given endpoints. 24. 2, 4 4,2A B 25. 3,5 1,1A B Given endpoint A and midpoint M of AB find the other endpoint. 26. 0,0 2, 3A M 27. 1,4 3,1A M 28. Calculate to find which point A or B is farthest from the origin (0,0). A(4, 3) or B(-1, 5)? 10 HW: 1.4 Angle Measurement Write three names for the angle shown. Then name the vertex and the sides of the angle. 1. 2. 3. Classify the angle with the given measure as acute, obtuse, right, or straight. 4. 115m A 5. 85m A 6. 90m A 7. 170m A Give another name for the angle in the diagram. Tell whether the angle appears to be acute, obtuse, right, or straight. 8. JKN 9. KMN 10. PQM 11. JML 12. QPN 13. PLK 14. List all of the angles have S as a vertex. 15. Name a straight angle. 16. Name an obtuse angle. 17. Does SRU appear to be obtuse, right, acute, or straight? 18. If the m 3 =48 and m 4 =23 then find the m RUT. 19. If m 6 is 177 the find m 2. Find the indicated angle measure. 20. m PRS 21. m EFG 22. m WXZ 11 3 0 12 Use the given information to find the indicated angle measure. 23. 24. 25. 26. In the diagram BD bisects ABC. Find mABC. 27. 30. 28. 13 29. 14 HW: 1.5 Angle Relationships Using the figure below list all of the following that apply to each pair of angles: adjacent, vertical, complementary, supplementary, and linear pair. 1. 1 and 2 2. 1 and 4 3. 4 and 5 4. 1 and 5 Use the figure below to answer questions 5-10 5. Name one pair of complementary angles 6. Name two angles that make a linear pair 7. Name one pair of vertical angles. 8. If m 4=43◦, then find the m 2. 9. If m 2=33◦, then find the m 5. 10. If m 2=37◦, then find the m 3. Refer to the figure below and answer the following questions. 11. If mABC =71◦, then find mCBD. 12. If mDBC =23, then find the mCBA. 13. If mABD = 2x-7, then find x. 14. If mABC = 3x+12 and mCBD =x-8, then find x. 15. If m 1 is twice the measure of its complement ( 2), then determine the measure of each angle. 16. If m 3 is five times the measure of its supplement, then determine the measure of each angle. Refer to the figure below and answer the following questions. 15 2 4 17. If mABC =136, then find the mCBD. 18. If mABC=7x-3 and mCBD =2x+12, then find x. 19. If mABC =119, then find mCBD. 20. If mABC=5x+5 and mCBD=x+15, then find x. Find x and determine if AB CD . Explain why. Refer to the pictures below and find the missing angles. 16 HW: Ch 1 Review Use the diagram answer the following questions. 9. 10. J is between H and K. Find the length of each segment using the following expressions. HJ = 5x – 4 JK = 8x - 10 HK = 15x - 20 11. 17 2 0 12. Given the endpoints of a segment, find the midpoint. A (6, -3) and B (10,5) 13. Given an endpoint and the midpoint of a segment, find the other endpoint. R (8,0), M(4,-5) 14. Determine if the segments are congruent. 15. Classify each angle as acute, obtuse, right or straight. 16. 17. BD bisects ABC. Given that (4 15)ABD x and ( 2 120)ABC x find x. 18. Solve for x and y. Show all equations and work! 19. The following angles are complementary. Find their measures. 20. Tell whether the angles are vertical angles, a linear pair, or neither. 18 19