Chapter Test. Form A. 67 Holt Geometry. Name Date Class. Circle the best answer. 1. What type of triangle is ABC? 6. If KLM RST, find the value of x.

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1 Form A Circle the best answer. 1. What type of triangle is ABC? If KLM RST, find the value of x. A acute B equiangular C obtuse D right 2. How many sides must be congruent in an isosceles triangle? A at least 2 B all 3 3. Which pair of angle measures CANNOT be the acute angles of a right triangle? A 29 and 61 B 30 and 60 C 38 and 53 D 5 and 5. What is macd? 50 A 100 B Given: TUV TWV. What is the value of x? A 20 B A 18 B 5 7. Given: A D, B E, C F, AB DE, BC EF, and CA FD. Which is a correct congruence statement? A BCA DEF B ABC DEF Use the figure for Exercises 8 and Which value for x proves that ABC DEF by SSS? A 7 B What additional information would allow you to prove the triangles congruent by SAS? A E D B D C C D A D F C 67 Holt Geometry

2 Form A continued Use the figure for Exercises 10 and What is the value of x? 10. Which postulate or theorem can you use to prove ABE and CDE? A SSS B SAS C ASA D AAS 11. What additional information will prove ABE CDE by HL? A AB CD B AE CE 12. To write a coordinate proof, you position a right isosceles triangle in the coordinate plane. The legs measure two units. What is the best position for the vertex angle? A (0,0) B (0,2) C (2, 0) D (2, 2) 13. Given: ABCD is a square with vertices A(0,0), B(0, ), C(, ), and D(,0). In a coordinate proof, what information would be used to prove AB CD if you do NOT use the distance formula? A x-coordinate of A, x-coordinate of C B y-coordinate of A, y-coordinate of C C y-coordinate of A, x-coordinate of C D x-coordinate of A, y-coordinate of C A 22.5 B 30 C 5 D 60 Use the figure for Exercises 15 and What postulate or theorem proves HG FG? A Isosceles Triangle Theorem B Converse of Isosceles Triangle Theorem 16. If FGJ HGJ, what reason justifies the statement HGJ FGJ? A ASA B Reflex. Prop. of C Def. of bisects D CPCTC 68 Holt Geometry

3 Form B Circle the best answer. 1. Classify the triangle A isosceles acute C scalene acute B isosceles obtuse D scalene obtuse Use the figure for Exercises 2 and Which is NOT a correct classification for the triangle? F acute H isosceles G equiangular J scalene 3. What is the length of side BC? A 3 C 10 B 8 D 2 Use the figure for Exercises and 5. (8 18) (6 ) (20 ). What is mklm? F 3 H 2 G 22 J 6 5. What is mm? A 0.2 C 26 B D 6 6. What is the mu? F 5 H 0 G 15 J Two congruent triangles have the following corresponding parts: RS UV, RT UW, and R U. Which is NOT necessarily a correct congruence statement? A RST UVW B STR VWU C TRS VWU D TRS WUV 8. KLM RST. ml (3x 15) and ms (6x 3). What is the value of x? F 2 H 6 G J 27 Use the figure for Exercises If AD 5y 7 and BC 7y 3, what must the value of y be to prove AED CEB by the SSS Postulate? A 2 C 17 B 5 D What postulate or theorem justifies the congruence statement ABE CDE? F SSS G SAS H ASA J AAS 69 Holt Geometry

4 Form B continued 11. If B and C are right angles, what additional congruence statement would allow you to prove DCB ABC by the ASA postulate? A DBC ACB B BDC CAB C AB DC D AC DB 12. If A and C are right angles and AD BC, what postulate or theorem justifies the congruence statement BCD DAB? F SAS G ASA H AAS J HL 13. A right triangle with leg lengths of and 3 units has to be positioned in the coordinate plane to write a coordinate proof. Which set of coordinates would make the proof easier to complete? A (, 0), (0, 0), (, 3) B (3, 0), (0, 0), (, 0) C (0, ), (0, 0), (3, 0) D (0, ), (0, 0), (3, 0) 1. Which of the following would you find most useful in giving a coordinate proof that two triangles are congruent by SSS? F Distance Formula H CPCTC G Midpoint Formula J Slope Formula 15. What is the value of x? ( 12) A 12 C 18 B 19.5 D 60 Use the partially completed two-column proof for Exercises Given: GJ bisects FGH, FG HG Prove: FJ HJ Proof: Statements 1. GJ bisects FGH. 1. Given Reasons 2. FGJ HGJ 2. Def. of bisector 3. FG HG 3. Given. F H.? 5. FGJ HGJ 5.? 6. FJ HJ 6.? 16. Which reason belongs in Step? F Isosc. Thm. G Conv. of Isosc. Thm. H ASA J Def. of bisector 17. Which reason belongs in Step 5? A Isosc. Thm. B ASA C CPCTC D HL 18. Which reason belongs in Step 6? F Isosc. Thm. G ASA H CPCTC J Def. of bisector 70 Holt Geometry

5 Circle the best answer. 1. Which best describes ABC with vertices A(2, 1), B(0, ), and C(2, 1)? A acute B equiangular C obtuse D right 2. Which is a correct classification of DEF with vertices D(3, 2), E(2, 3), and F(1, 0)? F equilateral G isosceles H scalene J Not here 3. If the acute angles of a right triangle are congruent, which statement is NOT true? A Both acute angles measure 5. B Only one exterior measures 90. C Only one exterior measures 135. D Two exterior angles measure What is the value of x? 122 Form C 139 F 1 H 99 G 58 J QRS STQ, QS x 2 10 and SQ 2x 2. What is the value of x? A C 2 B 2 D 6. ABC DEF. What information is NOT needed to find the perimeter of ABC if you are given all four lengths below? Use the partially completed two-column proof for Exercise 7. Given: Prove: GHF MOL Proof: Statements 1. GF ML, FH LO, GH MO 1. Given Reasons 2. F L 2.? 3. H O 3. Given. G M.? 5. GHF MOL 5.? 7. Which reason does NOT belong in the proof? A Def. of s B Third Thm. C Rt. Thm. D CPCTC Use the figure for Exercises F DE G BG H CF J EF 8. AB y 2 3, DC 3y 1, EB 3y 1, ED y 2 1, AE y 2, CE 2y. What value of y proves AEB CED by the SSS Postulate? F 2 H 1 G 1 J 2 71 Holt Geometry

6 9. What information would allow you to prove AED CEB by SAS? A E is the midpoint of DB. B E is the midpoint of AC. C E bisects AC. D E bisects both DB and AC. 10. If ADC and ABC are right angles, AC BD, and AB DC, which postulate or theorem proves ABC CDA? F SSS H ASA G SAS J HL 11. If AD BC and ABD CDB, which postulate or theorem could be used to prove ABD CDB? A SAS B ASA Form C continued C SSS D HL 12. Given: ABC with vertices A(5, 2), B(5, 7), and C(1, 2). Which set of coordinates best repositions the triangle to make a coordinate proof easier? F (0, 0), (, 0), and (, 5) G (0, 0), (, 0), and (0, 5) H (0, 0), (0, ), and (5, 0) J (0, 0), (, 0), and (0, 5) 13. If the height of a right triangle is n units and the base is m units, which statement is NOT true? A The midpoint of the hypotenuse is (m, n). B A(0, 0), B(m, 0), and C(0, n) can represent the vertices. C The midpoint of the hypotenuse is m 2, n 2. D The slope of the hypotenuse is n m. 1. What is mdac? F 30 G 5 H 60 J Not here Use the partially completed two-column proof for Exercises 15 and 16. Given: JK LK ; JYL and LXJ are rt.. Prove: JY LX Proof: Statements Reasons 1. KJL KLJ 1.? 2. JL LJ 2.? 3. JYL and LXJ are rt.. 3. Given. JYL LXJ.? 5. JYL LXJ 5.? 6. JY LX 6.? 15. Which justification belongs in Step 1? A Isosc. Thm. C Rt. Thm. B Reflex. Prop. of D CPCTC 16. Which justification belongs in Step 6? F Isosc. Thm. G HL H Rt. Thm. J CPCTC 72 Holt Geometry

7 Form A Use the figure for Exercises 1 and Complete the statement. Two triangles are congruent if and only if their angles and sides are congruent. 1. Classify the triangle by its angle measures. 2. Classify the triangle by its side lengths. 3. Complete the sentence. All of the angles in an equilateral triangle measure. Use the figure for Exercises 8 and What value of x proves ABC DEF by SAS? 27. What is the measure of 1? If AB DE, what additional congruence statement is needed to prove ABC DEF by SSS? 5. Given: GHJ NOP. What is the value of x? If KLM RST, what is the value of x? Use the figure for Exercises 10 and Write True or False. You can use AAS to prove ABE CDE What additional congruence statement is needed to prove ABE CDE by HL? 73 Holt Geometry

8 Form A continued 12. Write True or False. To give a coordinate proof about a right triangle, it is a good idea to position the vertex of the right angle at (0, 0) so that the legs are on the positive sides of the axes. 15. What postulate or theorem proves K M? 13. Write True or False. The Midpoint Formula is used in the coordinate proof to prove the statement EF 1 2 RS. 16. Write True or False. Given: ABC and DEF. To use CPCTC to prove A D, you must first prove ABC DEF. 1. Find the value of x. ( 12) 7 7 Holt Geometry

9 Form B Use the figure for Exercises 1 and Classify ABD by its angle measures. right 2. Classify ABC by its side lengths. equilateral 3. The measure of the smallest angle of a right triangle is 27. What is the measure of the second to smallest angle? 63. Find the measure of RST. (5 ) (8 ) JKL MNP, KL 21x 2, NP 20x, LJ 15x, PM 13x. Find LJ Given: TUV TWV. Find mu and UV. (9 6) (7 22) mu 120; UV Given: 5 6, 3, DE FE, FG DG, GE GE. Provide an additional statement and a reason for that statement to prove DEG FEG by the definition of congruent triangles ; Third Thm. Use the figure for Exercises If AB 3x 7 and DC 2x 1, what value of x proves AEB CED by the SSS Postulate? x 8 9. What postulate or theorem proves AED CEB? SAS 10. If DAB ADC, what additional congruence statement do you need to prove DAB ADC by the ASA Postulate? ADB DAC 11. If ABC and CDA are right angles and AB CD, what postulate or theorem proves ABC CDA? HL 75 Holt Geometry

10 Use the Given information for Exercises 12 and 13. Given: An isosceles triangle ABC with AB BC and a perpendicular bisector BD from B to AC. 12. Position the figure in the coordinate plane and assign coordinates to each point so proving that the area of ABD is equal to the area of CBD using a coordinate proof would be easier to complete. Possible answer: A(2, 0), B(0, ), C(2, 0), D(0,0) 13. Write a coordinate proof to prove that the area of ABD is equal to the area of CBD. Possible answer: ABD is a right triangle with base AD and height BD. CBD is a right triangle with base CD and height BD. area of ABD 1 2 bh 1 ()(2) square units 2 area of CBD 1 Form B continued 2 bh 1 ()(2) square units 2 The area of ABD is equal to square units, which equals the area of CBD. 1. Find the value of x. x 25 (3 5) 2 Use the figure and the partially completed two-column proof for Exercises 15 and 16. Given: BAC BCA Prove: AD Proof: CE Statements 1. BAC BCA 1. Given 2. BA Reasons BC 2.? 3. D and E are right. 3. Given (diagram). DB EB. Given (diagram) 5. DBA EBC 5. HL Congruence Thm. 6. AD CE 6.? 15. What is the justification for Step 2? Conv. of Isosc. Thm. 16. What is the justification for Step 6? CPCTC 76 Holt Geometry

11 Form C Use the figure for Exercises 1 and Prove TUV TWV by using the definition of congruent triangles Classify ABC by angle measures. 2. Classify ABD by side lengths. Use the figure for Exercises 3 and. 3 (2 10) (2 10) 3. What is mt?. What is the value of y? Use the figure for Exercises If AD BC, write a statement about point E that would allow you to prove AED CEB by the SSS Postulate. 5. Given QRS STQ, R x 2, and T 3x 2 3x. What is mr? 9. Suppose AE CE and BE DE. What postulate or theorem will allow you to prove BEA DEC? 6. Given QRS STQ, RS 3x 3, TQ 2x 2, and QR x 2 2. What is the length of side ST? 10. Write True or False. If ABC and DCB are right angles and AD BC, you can prove ABC DCB. 11. DAB and BCD are right angles. Write a single congruence statement about two segments that would allow you to conclude that DAB BCD. What theorem or postulate would justify the conclusion? 77 Holt Geometry

12 Form C continued 12. A triangle has vertices P(a, b), Q(c, d ), and R(e, f ). You are asked to prove that the image PQR of PQR after reflection across the y-axis is congruent to the preimage. What coordinates should you use for the vertices of PQR? 13. Assign variables as the coordinates and write a coordinate proof. Given: Square ABCD with side length of d units Prove: AC BD Use the figure and the partially completed two-column proof for Exercises 15 and 16. Given: RU TV, RS TS Prove: RV TU Proof: 1. Statements RS TS Reasons 1. Given 2. SRT STR 2.? 3. msrt mstr 3. Def. of. mrtv 180 mstr 5. mtru 180 mstr. Lin. Pair Thm. 5. Lin. Pair Thm. and Subst. (Step 2) 6. mrtv mtru 6. Subst. Prop. of 7. RTV TRU 7. Def. of 1. What is the value of x? 8. RT RT 8. Reflex. Prop. of 9. RU TV 9. Given 10. RTV TRU 10.? 11. RV UT 11.? 15. What reason belongs in Step 2? 16. What reason belongs in Step 11? 78 Holt Geometry

13 Answer Key continued Section Quiz: Lessons - Through B 6. G 2. J 7. C 3. D 8. H. J 9. D 5. D 10. H Form A: Multiple Choice 1. C 9. D 2. A 10. C 3. C 11. B. B 12. A 5. A 13. B 6. A 1. B 7. B 15. B 8. A 16. D Form B: Multiple Choice 1. C 7. C 13. D 2. J 3. B. J 5. C 6. J 8. G 9. B 10. G 11. A 12. J 1. F 15. A 16. F 17. B 18. H Form C: Multiple Choice 1. A 9. D 2. H 10. J 3. C 11. B. H 12. H 5. A 13. A 6. G 1. F 7. D 15. A 8. J 16. J Form A: Free Response 1. acute 2. isosceles corresponding AC DF 10. True 11. EC EA 12. True 13. False Isosceles Triangle Theorem 16. True Form B: Free Response 1. right 2. equilateral mu 120; UV ; Third Thm SAS 10. ADB DAC 11. HL 12. Possible answer: A(2, 0), B(0, ), C(2, 0), D(0,0) 257 Holt Geometry

14 Answer Key continued 13. Possible answer: ABD is a right triangle with base AD and height BD. CBD is a right triangle with base CD and height BD. Area of ABD 1 2 bh 1 ()(2) 2 square units. Area of CBD 1 2 bh 1 ()(2) square units. The area of 2 ABD is equal to square units, which equals the area of CBD. 1. x Conv. of Isosc. Thm. 16. CPCTC Form C: Free Response 1. equiangular, acute 2. scalene y units 7. Statements 1. TU TW, UV WV 1. Given Reasons 2. VT VT 2. Reflex. Prop. of 3. VTU VTW, UVT WVT 3. Given. U W. Third Thm. 5. TUV TWV 5. Def. of s 8. E bisects both AC and DB, or E is the midpoint of both AC and DB. 9. SAS 10. True 11. AD BC or AB DC ; HL 12. P(a, b), Q(c, d ), and R(e, f ) 13. Possible answer: Use vertices A(0, 0), B(0, d ), C(d, d ), and D(d, 0), where d AC (d 0) 2 (d 0) 2 2d 2 d 2 BD (d 0) 2 (0 d) 2 2d 2 d 2 AC BD by the Subst. Prop. of 15. Isosceles Triangle Theorem 16. CPCTC Performance Assessment 1. B(8, 5) 2. Def. of midpoint 3. AE : 3 ; EB : 3 ; BD : 3 ; DC : 3. Yes; since 3 3 1, AE EB, so maeb 90. Also, since 3 BD DC, so mcdb Possible answer: Show that AE or EB DB by using the Distance Formula. 6. CPCTC 1, 3 CD 258 Holt Geometry