Name: Class: Date: 5. Shown below is an illustration of the.

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1 Name: Class: Date: StudyGuide Unit 7 1. Determine if there is enough information to prove each pair of triangles are congruent by SSS or SAS. Write the congruence statements to justify your reasoning. a. PRT? TVP b. XWA? YZA 2. Refer to the figure below. ABC. 5. Shown below is an illustration of the. a. CDE b. EDA c. ACE d. EDC 3. A building casts a shadow 104 meters long. At the same time, a pole 4 meters high casts a shadow 8 meters long. What is the height of the building? a. AA Similarity Postulate b. SAS Congruence Theorem c. SSS Similarity Theorem d. SAS Similarity Theorem 4. A building casts a shadow 180 meters long. At the same time, a pole 4 meters high casts a shadow 12 meters long. What is the height of the building? 1

2 Name: 6. State the postulate or theorem that can be used to prove that the two triangles are similar. 9. Identify the congruent triangles. How do you know they are congruent? 7. In the figure, CAN is isosceles, Q is the midpoint of AC, and V is the midpoint of AN. What information is needed to prove CQH NVH? 10. Given: LMN UVW. Complete the statements. A. UW B. LMN 11. What is the angle measure of each interior angle of a regular polygon with 42 sides? a b c d a. AQH AVH b. QH VH and CH NH c. QH VH and QHC VHN d. HCN HNC and QHC VHN 8. If AC is parallel to DF, what is the measure, in degrees, of ABD? True or False: 12. If two lines are intersected by a transversal and corresponding angles are supplementary, then the lines are parallel. 13. If two lines are intersected by a transversal and alternate interior angles are equal in measure, then the lines are parallel. 14. Given that ED BA = EC, find BC to the nearest tenth. BC The figure is not drawn to scale. a. 28 b. 72 c. 62 d. 38 a b c. 2.3 d

3 Name: 15. In QRS, QR=10, RS = 11, and SQ =12. In UVT, VT= 20, TU =24, and UV=24. State whether the triangles are similar, and if so, write a similarity statement. 20. List the sides of the triangles shown in order from greatest to least. 16. Which of the following is a property of all squares? a. No sides are parallel. b. Opposite sides are not congruent. c. Opposite vertex angles are not congruent. d. The diagonals bisect each other. 17. Which of the following is a property of all rectangles? a. The diagonals are perpendicular. b. The diagonals bisect the vertex angles. c. Opposite sides are congruent. d. Only one pair of opposite sides is parallel. 18. What is the relationship between two lines that are perpendicular to the same line? a. a, b, c, d, e b. a, c, b, e, d c. a, c, d, e, b d. Cannot be determined. 21. In triangles TUW and WXT, U and X are congruent. Andre wants to prove that these triangles are similar. Which of the following is a counterexample to show that triangles TUW and TXW are NOT similar? a. They are parallel. b. They are perpendicular. c. They bisect each other. d. They intersect each other. 19. In the figure shown, BC DE, AB = 7 yards, BC = 9 yards, AE = 10 yards, and DE = 18 yards. Find BD. a. U X, but UTW is not congruent to XWT b. U X, but UWT XTW and UTW XWT c. U X, but UWT UTW and XTW XWT d. UWT UTW, XTW XWT, but U is not congruent to X 3

4 Name: 22. Which of the following cannot be used to show that the right triangles shown are congruent? 25. One way to show that two triangles are similar is to show that. a. two angles of one are congruent to two angles of the other b. two sides of one are proportional to two sides of the other c. a side of one is congruent to a side of the other d. an angle of one is congruent to an angle of the other 26. Quadrilateral ABCD is a parallelogram. Justify each statement. a. KM RT and KL RS b. LM ST and KL RS c. K R and L S d. KM RT and K R 23. State the postulate or theorem that can be used to prove that the two triangles are similar. a. AB DC b. DE BE c. ADC ABC 24. Which pair of lines is parallel if 4 is congruent to 2? 27. State two postulates or theorems that can be used to conclude that AOB COD. 4

5 Name: 28. Given: PQ BC. Find the length of AC. 32. Which triangle is NOT similar to any of the others? a. b. c. a. 24 b. 29 c. 27 d Select which statement is true about the relationship between the measures of A and B in the figure shown. d. 33. A map has a scale of 1 inch : 24 miles. If the 2 actual distance between the two cities is 480 miles, how far apart are they on the map? a. 20 inches b. 5 inches c. 10 inches d. 40 inches 34. In the figure, 6 and 3 are. a. The measure of A is greater than the measure of B. b. The measure of B is greater than the measure of A. c. The measure of A is equal to the measure of B. d. Cannot be determined without any other calculations. Determine if segments with the given measures could form a triangle. Use a complete sentence to justify your reasoning centimeters, 12 centimeters, 29 centimeters a. alternate exterior angles b. consecutive interior angles c. corresponding angles d. alternate interior angles 35. If RPQ JKL, then LJ yards, 25 yards, 41 yards 5

6 Name: 36. If triangles MNO and PQR are similar, which of the following must be true? 37. In the isosceles triangle shown, the measure of the base angle B is 52. What is the measure of BCD? a. NM QP = QR NO = MO PR = 1 b. N QRP, M QPR, O PQR c. N PQR, M QPR, O QRP d. NQ QO = RM PO = QP QR a. 52 b. 64 c. 116 d What value of x will make the two triangles similar? True or False: 39. If two parallel lines are intersected by a transversal, then consecutive interior angles are complementary. 41. In the figure shown, PS RQ. Which theorem can be used to prove SQR QSP? 40. If two parallel lines are intersected by a transversal, then alternate interior angles are congruent. a. SSS b. SAS c. AAS d. HL 6

7 Name: 42. Given AE Ä BD. Solve for x. 46. Jill draws triangle A B C by dilating triangle ABC by a scale factor of 3 using the origin as the center 2 of dilation. What are the coordinates of triangle A B C? 43. In QRS, QR=5, RS = 15, and m R =42. In UVT, VT=10, TU =30, and m T= 44. State whether the triangles are similar, and if so, write a similarity statement. 44. Triangle QRS has a perimeter of 55. If RT bisects angle R, what is the length of QT? a. A (6,4), B (2,8), C (4,10) b. A (9,4), B (3,8), C (6,10) c. A (6,9), B (6,9), C (10,12) d. A (9,6), B (3,12), C (6,15) 47. Points G, E, and P form a triangle. Also, GE TR, GP TQ, and PE QR. Which triangle is GEP congruent to? a. 10 b. 12 c. 15 d Michael draws a quadrilateral that has four congruent sides, but does not have congruent angles. Which best describes the quadrilateral formed? a. RTQ b. QTR c. TQR d. TRQ 48. If p Ä q, solve for x. a. rectangle b. rhombus c. square d. trapezoid 7

8 Name: 49. Given: BCD EFG. Find the length of BC. 53. In the figure shown, ABD and BCD are isosceles triangles and ABD CBD. Which theorem can be used to prove ABD CBD? 50. Given that a b, what is the value of x? (The figure may not be drawn to scale.) a. SSS b. SAS c. AAS d. HL 51. Which property is true of all parallelograms? a. Consecutive angles are congruent. b. The diagonals bisect each other. c. Consecutive sides are parallel. d. Opposite sides are perpendicular. 54. If the corresponding sides of two triangles are proportional, then. a. the triangles are right triangles b. the triangles are similar c. corresponding side lengths are equal d. the triangles are congruent 55. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? 52. Given CED and GEF are congruent vertical angles, CE = 1 3 GE, and ED = 1 EF, what theorem 3 could William use to show triangles CED and GEF are similar? a. Side-Side-Side Similarity Theorem b. Side-Angle-Side Similarity Theorem c. Angle-Angle Similarity Theorem d. Side-Side Similarity Theorem a. 8 2 b. 2 6 c. 5 3 d

9 StudyGuide Unit 7 Answer Section 1. ANS: a. PRT TVP by SSS. PR TV RT VP TP PT b. XWA YZA by SAS. XW YZ WA ZA W Z PTS: 1 REF: 5.7 NAT: G.CO.6 G.CO.7 G.CO.8 G.CO.9 G.CO.12 STA: G.CO.6 G.CO.7 G.CO.8 G.CO.9 G.CO.12 TOP: End Ch Test 2. ANS: D PTS: 1 DIF: Level B REF: HLGM0273 TOP: Lesson 4.3 Prove Triangles Congruent by SSS KEY: triangle congruent 3. ANS: 52 meters PTS: 1 DIF: Level B REF: MLGE0452 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 6.4 Prove Triangles Similar by AA KEY: word proportion similar triangle BLM: Application 4. ANS: 60 meters PTS: 1 DIF: Level B REF: GMC30831 NAT: NCTM 9-12.PRS.2 STA: GA MM3P1.a GA MM3P1.b GA MM3A7.a TOP: Lesson 6.4 Prove Triangles Similar by AA KEY: word proportion similar triangle BLM: Application 5. ANS: D PTS: 1 DIF: Level B REF: HLGM0654 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: triangle SAS BLM: Knowledge 6. ANS: SAS Similarity Theorem PTS: 1 DIF: Level B REF: MLGE0414 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar triangle theorem prove postulate BLM: Knowledge 1

10 7. ANS: B PTS: 1 REF: 6.3 NAT: G.CO.10 G.MG.1 STA: G.CO.10 G.MG.1 KEY: vertex angle Isosceles Triangle Base Theorem Isosceles Triangle Vertex Angle Theorem Isosceles Triangle Perpendicular Bisector Theorem Isosceles Triangle Altitude to Congruent Sides Theorem Isosceles Triangle Angle Bisector to Congruent Sides Theorem 8. ANS: A PTS: 1 DIF: Level C REF: MC NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: angle triangle sum parallel perpendicular BLM: Comprehension 9. ANS: WXZ WYZ; SSS PTS: 1 DIF: Level A REF: MIM20472 TOP: Lesson 4.3 Prove Triangles Congruent by SSS KEY: triangle congruent SSS 10. ANS: A. LN B. UVW PTS: 1 DIF: Level A REF: MLGE0123 TOP: Lesson 4.2 Apply Congruence and Triangles KEY: angle triangle segment congruent BLM: Knowledge 11. ANS: D PTS: 1 REF: 7.4 NAT: G.CO.9 G.SRT.8 G.MG.1 STA: G.CO.9 G.SRT.8 G.MG.1 KEY: interior angle of a polygon 12. ANS: False PTS: 1 DIF: Level B REF: MIM20443 TOP: Lesson 3.3 Prove Lines are Parallel KEY: angle parallel transversal corresponding BLM: Comprehension 13. ANS: True PTS: 1 DIF: Level B REF: MIM20442 TOP: Lesson 3.3 Prove Lines are Parallel KEY: line parallel transversal alternate interior BLM: Comprehension 14. ANS: B PTS: 1 DIF: Level B REF: MIM10384 TOP: Lesson 6.2 Use Proportions to Solve Geometry Problems KEY: proportion triangle length missing 15. ANS: not similar PTS: 1 DIF: Level B REF: PHGM1002 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: SSS similarity 16. ANS: D PTS: 1 REF: 7.6 NAT: G.CO.12 STA: G.CO ANS: C PTS: 1 REF: 7.6 NAT: G.CO.12 STA: G.CO.12 2

11 18. ANS: A PTS: 1 REF: 7.1 NAT: G.CO.11 G.CO.12 G.SRT.8 G.GPE.5 G.MG.1 STA: G.CO.11 G.CO.12 G.SRT.8 G.GPE.5 G.MG.1 KEY: Perpendicular/Parallel Line Theorem 19. ANS: 7 yd PTS: 1 DIF: Level B REF: MLGM0048 TOP: Lesson 6.6 Use Proportionality Theorems KEY: proportion similar triangles BLM: Knowledge -tx 20. ANS: A PTS: 1 REF: 3.2 NAT: G.CO.10 STA: G.CO.10 KEY: Triangle Inequality Theorem 21. ANS: A PTS: 1 REF: 4.1 NAT: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 STA: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 KEY: similar triangles 22. ANS: C PTS: 1 REF: 6.1 NAT: G.CO.6 G.CO.7 G.CO.8 G.CO.10 G.CO.12 G.MG.1 STA: G.CO.6 G.CO.7 G.CO.8 G.CO.10 G.CO.12 G.MG.1 KEY: Hypotenuse-Leg (HL) Congruence Theorem Leg-Leg (LL) Congruence Theorem Hypotenuse-Angle (HA) Congruence Theorem Leg-Angle (LA) Congruence Theorem 23. ANS: AA Similarity Postulate PTS: 1 DIF: Level A REF: HLGM0650 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar triangle theorem prove postulate 24. ANS: c and d BLM: Knowledge PTS: 1 DIF: Level B REF: MC NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.3 Prove Lines are Parallel KEY: line angle parallel 25. ANS: A PTS: 1 DIF: Level B REF: HLGM0641 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar triangle rule BLM: Knowledge 26. ANS: a. Opposite sides of a parallelogram are congruent. b. The diagonals of a parallelogram bisect each other. c. Opposite angles of a parallelogram are congruent. PTS: 1 REF: 7.2 NAT: G.CO.11 G.CO.12 G.GPE.5 G.MG.1 STA: G.CO.11 G.CO.12 G.GPE.5 G.MG.1 TOP: Mid Ch Test KEY: Parallelogram/Congruent-Parallel Side Theorem 3

12 27. ANS: SAS and SSS Congruence Postulates PTS: 1 DIF: Level B REF: MLGE0233 TOP: Lesson 4.4 Prove Triangles Congruent by SAS and HL KEY: triangle congruent SSS SAS 28. ANS: C PTS: 1 DIF: Level B REF: PHGM1023 TOP: Lesson 6.6 Use Proportionality Theorems KEY: proportion similar triangle parallel side-splitter BLM: Knowledge -tx 29. ANS: D PTS: 1 REF: 3.2 NAT: G.CO.10 STA: G.CO.10 KEY: Triangle Inequality Theorem 30. ANS: No. The Triangle Inequality Theorem states that any two sides of a triangle must have a sum greater than the length of the third side. Because = 24 and 24 < 29, these given measures cannot form a triangle. PTS: 1 REF: 3.2 NAT: G.CO.10 STA: G.CO.10 TOP: End Ch Test KEY: Triangle Inequality Theorem 31. ANS: Yes. The sum of the lengths of any two sides of this triangle are greater than the length of the third side. PTS: 1 REF: 3.2 NAT: G.CO.10 STA: G.CO.10 TOP: End Ch Test KEY: Triangle Inequality Theorem 32. ANS: D PTS: 1 DIF: Level B REF: MLGE0169 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 6.4 Prove Triangles Similar by AA KEY: similar triangle BLM: Comprehension 33. ANS: C PTS: 1 DIF: Level B REF: MC NAT: NCTM 9-12.MEA.1.a TOP: Lesson 6.2 Use Proportions to Solve Geometry Problems KEY: ratio word proportion BLM: Application 34. ANS: B PTS: 1 DIF: Level B REF: MGEH0023 TOP: Lesson 3.1 Identify Pairs of Lines and Angles KEY: angles interior consecutive BLM: Knowledge 35. ANS: QR PTS: 1 DIF: Level A REF: HLGM0258 TOP: Lesson 4.2 Apply Congruence and Triangles KEY: triangle congruent BLM: Knowledge 36. ANS: C PTS: 1 REF: 4.1 NAT: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 STA: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 KEY: similar triangles 37. ANS: D PTS: 1 REF: 3.1 NAT: G.CO.10 G.MG.1 STA: G.CO.10 G.MG.1 KEY: Triangle Sum Theorem remote interior angles of a triangle Exterior Angle Theorem Exterior Angle Inequality Theorem 4

13 38. ANS: 60 PTS: 1 DIF: Level B REF: HLGM0640 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar triangle 39. ANS: False PTS: 1 DIF: Level B REF: MGEO0047 TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: conditional parallel logic co-interior 40. ANS: True PTS: 1 DIF: Level A REF: MIM20427 TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: conditional parallel logic alternate interior BLM: Knowledge 41. ANS: D PTS: 1 REF: 6.1 NAT: G.CO.6 G.CO.7 G.CO.8 G.CO.10 G.CO.12 G.MG.1 STA: G.CO.6 G.CO.7 G.CO.8 G.CO.10 G.CO.12 G.MG.1 KEY: Hypotenuse-Leg (HL) Congruence Theorem Leg-Leg (LL) Congruence Theorem Hypotenuse-Angle (HA) Congruence Theorem Leg-Angle (LA) Congruence Theorem 42. ANS: 6 PTS: 1 DIF: Level B REF: MLGM0049 TOP: Lesson 6.6 Use Proportionality Theorems BLM: Knowledge -tx 43. ANS: not similar KEY: similar triangle parallel PTS: 1 DIF: Level B REF: PHGM1001 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: similar SAS 44. ANS: A PTS: 1 REF: 4.3 NAT: G.GPE.7 G.SRT.4 G.SRT.5 STA: G.GPE.7 G.SRT.4 G.SRT.5 KEY: Angle Bisector/Proportional Side Theorem Triangle Proportionality Theorem Converse of the Triangle Proportionality Theorem Proportional Segments Theorem Triangle Midsegment Theorem 45. ANS: B PTS: 1 REF: 7.6 NAT: G.CO.12 STA: G.CO ANS: D PTS: 1 REF: 4.1 NAT: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 STA: G.SRT.1.a G.SRT.1.B G.SRT.2 G.SRT.5 G.MG.1 KEY: similar triangles 5

14 47. ANS: D PTS: 1 REF: 6.2 NAT: G.CO.10 G.MG.1 STA: G.CO.10 G.MG.1 KEY: corresponding parts of congruent triangles are congruent (CPCTC) Isosceles Triangle Base Angle Theorem Isosceles Triangle Base Angle Converse Theorem 48. ANS: 14 PTS: 1 DIF: Level B REF: AGEO0610 TOP: Lesson 6.6 Use Proportionality Theorems BLM: Knowledge -tx 49. ANS: 40 KEY: similar triangle length side PTS: 1 DIF: Level B REF: GGEO0704 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: ratio solve proportion figure similar triangle BLM: Comprehension 50. ANS: 70 PTS: 1 DIF: Level B REF: MCT90006 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: angle Parallel Postulate BLM: Analysis 51. ANS: B PTS: 1 REF: 7.6 NAT: G.CO.12 STA: G.CO ANS: B PTS: 1 REF: 4.2 NAT: G.SRT.3 G.SRT.5 STA: G.SRT.3 G.SRT.5 KEY: Angle-Angle Similarity Theorem Side-Side-Side Similarity Theorem included angle included side Side-Angle-Side Similarity Theorem 53. ANS: B PTS: 1 REF: 6.3 NAT: G.CO.10 G.MG.1 STA: G.CO.10 G.MG.1 KEY: vertex angle Isosceles Triangle Base Theorem Isosceles Triangle Vertex Angle Theorem Isosceles Triangle Perpendicular Bisector Theorem Isosceles Triangle Altitude to Congruent Sides Theorem Isosceles Triangle Angle Bisector to Congruent Sides Theorem 54. ANS: B PTS: 1 DIF: Level A REF: HLGM0644 TOP: Lesson 6.5 Prove Triangles Similar by SSS and SAS KEY: side corresponding proportional BLM: Knowledge 55. ANS: D PTS: 1 DIF: Level B REF: MGEH0026 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 3.2 Use Parallel Lines and Transversals KEY: parallel transversal BLM: Analysis 6