University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2019
Views:

334

Pages:

2
Author:

Sean Horton

CHAPTER 6 STUDY GUIDE In Exercises 1-4, find the indicated measure. Explain your reasoning. 1.AD 5. 2. GJ 3. PQ 4. mDGF 5.) Find the coordinates of the circumcenter of the triangle with the given vertices. J 6, 0, K 0, 0, L0, 4 In Exercise 6, P is the incenter of triangle QRS. Use the given information to find the indicated measure. 6. PJ  4 x  8, PL  x  7 Find PK . In Exercises 7-8, point P is the centroid of triangle ABC. Use the given information to find the indicated measures. CP  16 7. 8. BL  12 Find BP and PL. Find PL and CL. 9) Find the coordinates of the centroid: Q2, 6, R4, 0, S 10, 6 In Exercises 10-14, use the graph of triangle ABC. 10. In triangle ABC. show that the midsegment ED is parallel to BC and that ED  1 BC. 2 11. Find the coordinates of the endpoints of midsegment EF , which is opposite AC. 12. Show that EF is parallel to AC and that EF  1 AC. 2 13. State the coordinates of the endpoints of midsegment DF . 14. Show that DF is parallel to AB and DF  1 AB. 2 In Exercises 1 5- 17 , use triangle QRS, where A, B, and C are the midpoints of the sides. 15. When AB  16, what is QS? 16. When CA  3x  1 and SR  5x  4, what is CA? 17. When QR  5x  2 and CB  2 x  5, what is AR? # 18-19, list the angles from smallest to largest. # 20-21, list the sides from shortest to longest. 18. 20. 19. 21. In Exercises 22-23, is it possible to construct a triangle with the given side lengths? Explain. 22. 15, 37, 53 23. 9, 16, 8 In Exercises 24-27, copy and complete the statement with , , or  . Explain your reasoning. 24. AC _____ DF ANSWER KEY: 1. 20 7. BP=8 and PL=4 BC=2√10 13. D(2,1) F(4,1) 18. N,L,M 24. AC >DF 25. mHGI _____ mIGJ 26. m1 _____ m2 27. KL _____ MN 2. GJ 17 3. PQ 14 4. mDGF 76 5. (3,2) 6. 12 8. Find PL=8 and CL=24 9. (4,4) 10. Slope of BC=-3 and EC= -3 ED=√10 11. E(1,4) F(4,1) 12. Slope of EF=-1 and AC= -1 EF=3√2 AC=6√2 14. Slope of BC=0 and EC= 0 DF=2 AB=4 15. 32 16. 17 17. 21 19. F=D, E 20. AB,AC,BC 21. QP,PR,QR 22. No 23. Yes 25. 26. 1<2 27. KL