Name———————————————————————— Lesson 4.4 Date ————————————— Study Guide For use with the lesson “Prove Triangles Congruent by SSS” goal Use the side lengths to prove triangles are congruent. Vocabulary Postulate 19 Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. example 1 Use the SSS Congruence Postulate J Prove that nJKL > nMLN. M Solution The marks on the diagram show that } } } } } } JK , KL > LN , and JL > MN . > ML K L N So, by the SSS Congruence Postulate, n JKL > n MLN. Exercises for Example 1 1. n ABD > n CDB 2. n XWY > n WZY B X Z 6 W C A 9 D 9 4 Y 3. n RST > n VUT 6 4. n FGH > n JHG S R G J T F V 5. n PQR > n RTS H U 6. n JKL > n MPN Q P K 6 T J S V R Lesson 4.4 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Decide whether the congruence statement is true. Explain your reasoning. 4 1 M L 2 5 N 4 P Geometry Chapter Resource Book 4-53 Name———————————————————————— Lesson 4.4 Date ————————————— Study Guide continued For use with the lesson “Prove Triangles Congruent by SSS” example 2 Congruent triangles in a coordinate plane Use the SSS Congruence Postulate to show that nABC > nCDE. y A(24, 2) E(1, 3) D(4, 1) 2 x 1 C(21, 0) B(23, 23) Solution Use the Distance Formula to show that corresponding sides are the same length. }}} 2 AB 5 Ï (23 2 (24)) 1 (23 2 2)2 } 5Ï 12 1 (25)2 5Ï 26 } }} CD 5 Ï (4 2 (21))2 1 (1 2 0)2 } 5 Ï 52 1 12 } 5 Ï 26 } } So, AB 5 CD, and hence AB > CD . } 5Ï 22 1 32 5Ï 13 } }} DE 5 Ï (1 2 4)2 1 (3 2 1)2 } 5 Ï (23)2 1 22 } 5 Ï 13 } } So, BC 5 DE, and hence BC > DE . }}} CA 5 Ï (24 2 (21))2 1 (2 2 0)2 }} EC 5 Ï (21 2 1)2 1 (0 2 3)2 }} } 2 5 Ï (22)2 1 (23) } 5 Ï 13 5Ï (23)2 1 22 5Ï 13 } } } So, CA 5 EC, and hence CA > EC . So, by the SSS Congruence Postulate, you know that n ABC > n CDE. Exercise for Example 2 7. Prove that n ABC > n DEF. y Lesson 4.4 F(0, 3) B(22, 0) 1 1 E(2, 0) A(24, 21) 4-54 D(4, 1) Geometry Chapter Resource Book C(0, 23) x Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. }}} 2 BC 5 Ï (21 2 (23)) 1 (0 2 (23))2 answers Teaching Guide 1. Sample answer: Two triangles support each horizontal pole. This helps the vertical pole and the horizontal pole to remain perpendicular. 2. Sample answer: The roof is stable because it is triangular; that is, it is less likely to cave in. Also, the two vertical boards in the internal structure of the roof create more triangles, which make the roof even more stable. 3. Sample answer: The two triangles formed at the base of the basketball hoop stand help the pole remain vertical and help the base be more stable on the ground. 4. Sample answer: The two triangles in the structure of the bridgework add rigidity to the overall trapezoidal shape, which is not rigid by itself. Practice Level A 1. neither 2. corresponding angles 3. corresponding sides 4. neither 5. false; n IHJ ù n KHJ 6. true; SSS 7. false; n ACE ù n BFD 8. true; SSS 9. Stable; the figure forms triangles of fixed side lengths which cannot change shape by the SSS Congruence Postulate. 10. Not stable; there are many possible shapes for a four-sided figure with the given side lengths. 11. congruent 12. not congruent 13. yes; the corresponding sides are congruent. 14. no; the corresponding sides are not congruent. 15. The second gate door has a diagonal support that forms two triangles with fixed sides, and these triangles cannot change shape by the SSS Congruence Postulate. Practice Level B 1. true; SSS 2. true; SSS 3. true; SSS 4. congruent 5. not congruent 6. not congruent 7. congruent 8. Stable; the figure forms triangles of fixed side lengths which cannot change shape by the SSS Congruence Postulate. 9. Not stable; there are many possible shapes for a four-sided figure with the given side lengths. 10. Stable; the figure forms triangles of fixed side lengths which cannot change shape by the SSS Congruence Postulate. 11. Yes; the corresponding sides are congruent. A50 12. No; the corresponding sides are not congruent. 13. Given; Given; Reflexive Property of Congruence; SSS Congruence Postulate 14. Given; Given; Definition of midpoint; Reflexive Property of Congruence; SSS Congruence Postulate 15. The second picture frame is stable because the brace and the sides form triangles of fixed side lengths which cannot change shape by the SSS Congruence Postulate. Practice Level C 1. true; SSS 2. true; SSS 3. true; SSS 4. congruent 5. congruent 6. not congruent 7. not congruent 8. Stable; the figure forms triangles of fixed side lengths which cannot change shape by the SSS Congruence Postulate. 9. Not stable; there are many possible shapes for a four-sided figure with the given side lengths. 10. The triangle vertices do not correspond. Sample answer: n JHI ù n IKJ } } } } } } 11. HI ù JK ; IJ ù KH ; HJ ù HJ ; } } ; Z is the midpoint n HIJ ù n JKH 12. WX ù YX } } } } } ù YZ ; XZ ù XZ ; n WXZ ù n YXZ of WY ; WZ 13. x 5 3; Setting 2x 1 3 5 7x 2 12 and 2x 1 14 5 6x 2 7 yields x 5 3 in both equations. Study Guide 1. Yes, the corresponding triangle sides are } } } } À ZY , XY À WY congruent 2. No; WY 3. Yes, the corresponding triangle sides are congruent 4. Yes, the corresponding triangle sides are congruent 5. Yes, the corresponding triangle } } } } 6. No; JK À MP , JL À MN } sides are congruent } } } 7. AB 5 DE 5 Ï 5 so AB > DE } ; BC 5 EF 5 Ï 13 } } } } ; CA 5 FD 5 2Ï5 so CA > FD ; By so BC > EF the SSS Congruence Postulate, n ABC > n DEF. Real-Life Application 1. a. ∠ ADB b. ∠ CBA c. ∠ CDB d. ∠ ABD 2. a. Statements 1. ABCD is a square. } } 2. AB > CD } } AD > CB } } 3. BD > DB 4. n ABD > nCDB Reasons 1. Given 2. Def. of a square 3. Reflexive Property 4. SSS Congruence Postulate Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Lesson 4.4 Prove Triangles Congruent by SSS Geometry Chapter Resource Book CS10_CC_G_MECR710761_C4AK.indd 50 4/28/11 6:14:08 PM
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