Geometry Chapter 5 study guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A right triangle is placed in a convenient position in the first quadrant of a coordinate plane. Which is the missing label for the vertex? y a. 11 b. 12 c. 10 d. 5 (0,0) (u, 0) x a. b. c. d. 5. If is the perpendicular bisector of, then KGF. 2. In a triangle, a segment connecting the midpoints of two sides of the triangle is called a. a. shortcut b. midsegment c. centroid d. vertex 3. Solve for x given = and =. Assume B is the midpoint of midpoint of C and D is the a. KHF b. FKG c. d. KFH 6. In the diagram below, is the perpendicular bisector of. Then. B D A E a. 1 2 b. 4 c. 2 d. 1 4 a. b. c. d. 4. For the triangle shown, VS = 5 and VQ = 6. Then PQ =.
7.Given: is the perpendicular bisector of. Which statement is true? a. b. CM = BM c. is a right angle. d. C is the midpoint of 8. Given: bisects DAB. Find ED if and (not drawn to scale) Given:, ABE EBC 10. A median of is. a. 51 b. 540 c. 39 d. 21 9. bisects BOA,, and. Which statement is NOT true? a. b. c. d. 11. An altitude of is. a. b. c. d. 12. The medians of a triangle are concurrent. Their common point is the. a. centroid b. incenter c. orthocenter d. circumcenter a. b. AOE EAO c. d. AEO BEO Refer to the figure below.
13. is an altitude of. Therefore, is. a. right b. equilateral c. isosceles d. acute Short Answer 14. A right triangle is placed in a convenient position on the first quadrant of a coordinate plane. If and, find the distance between. 18. For the given triangle, state the relationships between and. (0,a) y (0,0) (b, 0) 15. Using the diagram, give the coordinates of M if it is a midpoint. x In the diagram, are midsegments of triangle ABC. Find the value of the variable if. 19. x 20. y 16. How many midsegments does a triangle have? 17. Solve for x given = and =. Assume B is the midpoint of and D is the midpoint of 21. z 22. is the perpendicular bisector of. If OM = 4 and LN = 6, then LO = and MN =. Explain your solutions. C B D A E 23. The perpendicular bisectors of a triangle all pass through what point?
24.Given: is the bisector of. Name three things that you can conclude. 28. If the incenter of a triangle is also its circumcenter, what type of triangle is it? 29. In the diagram, X is the incenter of. Find XU. 25. Find AB. Is there enough information to show that D lies on the vertical line that passes through B? 30. Find the value of x. 26. Find the value of z. Is there enough information to show that D lies on the vertical line that passes through B? 31. 32. 27. Given: bisects RST. Find QR if and (not drawn to scale) 33. How many medians does a triangle have? True or False: 34. The medians of a triangle are always in the interior of the triangle. 35. The altitudes of a triangle are concurrent. What is the name of their common point?
Geometry Chapter 5 study guide Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: Level B REF: MLGE0006 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: triangle coordinate geometry position proof MSC: DOK 1 2. ANS: B PTS: 1 DIF: Level A REF: HLGM0388 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: triangle midpoint segment MSC: DOK 1 3. ANS: B PTS: 1 DIF: Level B REF: PHGM0015 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: triangle midsegment MSC: DOK 2 4. ANS: C PTS: 1 DIF: Level B REF: HLGM0389 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: triangle midsegment theorem MSC: DOK 2 5. ANS: A PTS: 1 DIF: Level B REF: HLGM0343 KEY: angle triangle perpendicular bisector MSC: DOK 2 6. ANS: C PTS: 1 DIF: Level B REF: MGEO0008 KEY: triangle isosceles congruent perpendicular bisector MSC: DOK 1 7. ANS: A PTS: 1 DIF: Level B REF: MHGM0083 KEY: perpendicular bisector MSC: DOK 1 8. ANS: C PTS: 1 DIF: Level B REF: PHGM0420 KEY: solve angle bisector MSC: DOK 2 9. ANS: B PTS: 1 DIF: Level B REF: HLGM0344 KEY: angle triangle perpendicular bisect MSC: DOK 2 10. ANS: B PTS: 1 DIF: Level B REF: MLGE0129 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle median MSC: DOK 1 11. ANS: C PTS: 1 DIF: Level B REF: MLGE0449 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle altitude MSC: DOK 1 12. ANS: A PTS: 1 DIF: Level A REF: HLGM0370 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle point median concurrent MSC: DOK 1 13. ANS: A PTS: 1 DIF: Level B REF: HLGM0373 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle altitude MSC: DOK 1
SHORT ANSWER 14. ANS: 85 PTS: 1 DIF: Level B REF: MLGE0051 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: distance triangle Pythagorean coordinate plane MSC: DOK 2 15. ANS: PTS: 1 DIF: Level B REF: MLGE0052 LOC: NCTM.PSSM.00.MTH.9-12.GEO.2.a TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: distance triangle midpoint MSC: DOK 2 16. ANS: 3 PTS: 1 DIF: Level B REF: MHST0001 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof MSC: DOK 1 17. ANS: 1 PTS: 1 DIF: Level B REF: PHGM0014 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof MSC: DOK 2 18. ANS: and KEY: triangle midsegment KEY: triangle midsegment PTS: 1 DIF: Level B REF: HLGM0392 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof MSC: DOK 2 19. ANS: 8 PTS: 1 DIF: Level B REF: 7f57ba13-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK 2 20. ANS: 2 PTS: 1 DIF: Level B REF: 7f57e123-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK 2 21. ANS: 15
PTS: 1 DIF: Level B REF: 7f580833-cdbb-11db-b502-0011258082f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK 2 22. ANS: LO = 4, MN = 6; LO = OM by definition of bisector and MN = LN by the Perpendicular Bisector Theorem. PTS: 1 DIF: Level B REF: MLGE0352 LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.b KEY: length perpendicular segment bisector MSC: DOK 2 23. ANS: Circumcenter PTS: 1 DIF: Level A REF: HLGM0374 KEY: triangle perpendicular bisector MSC: DOK 1 24. ANS: Any three of the following:,, M is the midpoint of, LMR, TMR, TMQ, LMQ are all right angles. PTS: 1 DIF: Level B REF: XEGS0306 KEY: perpendicular bisector MSC: DOK 2 25. ANS: ; no PTS: 1 DIF: Level B REF: 7f594148-cdbb-11db-b502-0011258082f7 KEY: perpendicular bisector theorem converse MSC: DOK 2 26. ANS: ; yes PTS: 1 DIF: Level B REF: 7f596858-cdbb-11db-b502-0011258082f7 KEY: perpendicular bisector theorem converse MSC: DOK 2 27. ANS: 125 PTS: 1 DIF: Level B REF: PHGM0410 NAT: NT.CCSS.MTH.10.9-12.G.SRT.8 KEY: solve angle bisector MSC: DOK 2 28. ANS: Equilateral PTS: 1 DIF: Level B REF: HLGM0380 LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.a KEY: triangle circumcenter incenter MSC: DOK 1 29. ANS:
PTS: 1 DIF: Level B REF: GEO.05.03.FR.08 KEY: Free Response angle bisector incenter length MSC: DOK 2 30. ANS: 7 PTS: 1 DIF: Level B REF: 7f840b14-cdbb-11db-b502-0011258082f7 KEY: angle bisector theorem converse MSC: DOK 2 31. ANS: 6 PTS: 1 DIF: Level B REF: 7f845934-cdbb-11db-b502-0011258082f7 KEY: angle bisector theorem converse MSC: DOK 2 32. ANS: 12 PTS: 1 DIF: Level B REF: 7f85b959-cdbb-11db-b502-0011258082f7 KEY: angle bisector theorem converse MSC: DOK 2 33. ANS: 3 PTS: 1 DIF: Level A REF: HLGM0376 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle medians MSC: DOK 1 34. ANS: True PTS: 1 DIF: Level B REF: MLGE0330 TOP: Lesson 5.4 Use Medians and Altitudes KEY: property triangle MSC: DOK 1 35. ANS: Orthocenter PTS: 1 DIF: Level A REF: HLGM0379 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle point altitude concurrent MSC: DOK 1