Geometry Chapter 5 study guide
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1 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 =.
2 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 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.
3 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?
4 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? 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?
5 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 ANS: B PTS: 1 DIF: Level B REF: MLGE0129 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle median MSC: DOK ANS: C PTS: 1 DIF: Level B REF: MLGE0449 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle altitude MSC: DOK ANS: A PTS: 1 DIF: Level A REF: HLGM0370 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle point median concurrent MSC: DOK ANS: A PTS: 1 DIF: Level B REF: HLGM0373 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle altitude MSC: DOK 1
6 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 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 ANS: 3 PTS: 1 DIF: Level B REF: MHST0001 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof MSC: DOK ANS: 1 PTS: 1 DIF: Level B REF: PHGM0014 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof MSC: DOK 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 ANS: 8 PTS: 1 DIF: Level B REF: 7f57ba13-cdbb-11db-b f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK ANS: 2 PTS: 1 DIF: Level B REF: 7f57e123-cdbb-11db-b f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK ANS: 15
7 PTS: 1 DIF: Level B REF: 7f cdbb-11db-b f7 TOP: Lesson 5.1 Midsegment Theorem and Coordinate Proof KEY: midsegment theorem MSC: DOK 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 ANS: Circumcenter PTS: 1 DIF: Level A REF: HLGM0374 KEY: triangle perpendicular bisector MSC: DOK 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 ANS: ; no PTS: 1 DIF: Level B REF: 7f cdbb-11db-b f7 KEY: perpendicular bisector theorem converse MSC: DOK ANS: ; yes PTS: 1 DIF: Level B REF: 7f cdbb-11db-b f7 KEY: perpendicular bisector theorem converse MSC: DOK ANS: 125 PTS: 1 DIF: Level B REF: PHGM0410 NAT: NT.CCSS.MTH G.SRT.8 KEY: solve angle bisector MSC: DOK 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 ANS:
8 PTS: 1 DIF: Level B REF: GEO FR.08 KEY: Free Response angle bisector incenter length MSC: DOK ANS: 7 PTS: 1 DIF: Level B REF: 7f840b14-cdbb-11db-b f7 KEY: angle bisector theorem converse MSC: DOK ANS: 6 PTS: 1 DIF: Level B REF: 7f cdbb-11db-b f7 KEY: angle bisector theorem converse MSC: DOK ANS: 12 PTS: 1 DIF: Level B REF: 7f85b959-cdbb-11db-b f7 KEY: angle bisector theorem converse MSC: DOK ANS: 3 PTS: 1 DIF: Level A REF: HLGM0376 TOP: Lesson 5.4 Use Medians and Altitudes KEY: triangle medians MSC: DOK ANS: True PTS: 1 DIF: Level B REF: MLGE0330 TOP: Lesson 5.4 Use Medians and Altitudes KEY: property triangle MSC: DOK 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
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