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Answer Key

Lesson 4.1

Practice Level B

1. sometimes 2. never 3. never 4. sometimes

5. scalene, obtuse 6. scalene, right

7. isosceles, acute

8.

9.

scalene; right triangle scalene; not a right triangle

10.

isosceles; not a right triangle

11. 30; right 12. 25; acute 13. 120; acute 14. 1318 15. 1008 16. 1258 17. 368 18. 1228 19. 1228 20. 388 21. mA 5 608, m B 5 308, m C 5 908 22. m A 5 608, m B 5 308, m C 5 908 23. 60, 30 24. 45, 51 25. 24, 66 26. scalene; right

Answer Key

Lesson 4.2

Practice Level B 1. Check student diagram; } AM ? C}D; A}T ? C}N; } MT ? D}N; A ? C; M ? D; T ? N 2. T 3. H}S 4. 488 5. 738 6. 5 cm 7. nJTM 8. nDEG ? nFGE; all corresponding sides and angles are congruent.

Answer Key

Lesson 4.3

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 Congru-

ence 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. 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.

Answer Key

Lesson 4.4

Practice Level B 1. ABC 2. BCD 3. ABD 4. BDA 5. DAB 6. CDB 7. not enough 8. enough 9. not enough 10. Yes, SAS Congruence Postulate 11. Yes, HL Congruence Theorem

12. not enough 13. } RM ? F}B 14. J ? D 15. } JM ? } DB or J}R ? } DF 16. Given; A}B ? } BE; Given; } CB ? } BD; Vertical Angles Theorem; SAS Congruence Postulate 17. Given; Alternate Interior Angles Theorem; Given; Reflexive Property of Congruence; SAS Congruence Postulate

Answer Key

Lesson 4.5

Practice Level B 1. } DF > } MO 2. D > M 3. D > M 4. } BC > } YZ or } AC > X}Z 5. B > Y 6. A > X 7. Yes, ASA Congruence Postulate; use } WL > } WL by Reflexive Property of Congruence

8. Yes, AAS Congruence Theorem; use TSN > USH by Vertical Angles Theorem

9. Yes, AAS Congruence Theorem

10. Yes, AAS Congruence Theorem

11. Yes, SAS Congruence Postulate

12. No; three pairs of congruent angles is insufficient to prove triangle congruence.

13. No; two angles and a non-included side are congruent, but the non-included sides are not corresponding

parts.

14. Two pairs of corresponding sides ( B}F ? } BD, E}F ? } ED ) and the corresponding included angles

( BFE ? BDE) are congruent.

15. Two ed sides

(p} AaDirs?of} CcFor)reasrepocnodnignrgueanntg.les

(

ADB

?

CFB,

BAD

?

BCF)

and

the

corresponding

includ-

16. Two pairs

cluded sides (

A} oFf c?orC} reDsp)oanrdeincgonagnrguleenst(.

ABF

?

CBD,

BAF

?

BCD)

and

the

corresponding

non-in-

17. 1. Given; 2. Corresponding Angles Postulate; 3. Given; 4. Corresponding Angles Postulate; Given; 5.

ASA Congruence Postulate 18. It is given that B ? D. By the Converse of Base Angles Theorem, A}C ? E}C. By the Vertical Angles Theorem, BCA ? DCE. nABC ? nEDC by the AAS Congruence Theorem.

Answer Key

Lesson 4.6

Practice Level B

1. n ABC ? nCDA; SAS

2. nTSU ? nVSU; AAS

3. nABD ? nCDB; SSS

4. nNKH ? nTMG; AAS

5. nABD ? nCBE; ASA

6. n ABC ? nSTA; AAS

7. Use the HL Congruence Theorem to prove that n DAB ? nBCD. Then use the fact that

corresponding parts of congruent triangles are congruent to prove that DAB ? BCD. 8. Because } ST i } RQ, PRQ ? / RST by the Corresponding Angles Postulate. Use the

ASA Congruence Postulate to prove congruent triangles are congruent to

tphraotvne tPhRatQ} ST??n} RRQST. .

Then

use

the

fact

that

corresponding

parts

of

9. Use the Distance Formula to find the side lengths of the triangles. Use the SSS Congruence Postulate to show that nABC ? nDEF. Then use the fact that corresponding parts of congruent triangles are congruent to prove that A ? D.

10. Use the Distance Formula to find the side lengths of the triangles. Use the SSS Congruence Postulate to show that n ABC ? nDEF. Then use the fact that corresponding parts of congruent triangles are congruent to prove that A ? D.

11. Given; Given; Definition of angle bisector; Reflexive Property of Congruence; SAS Congruence Postulate; Corresponding parts of congruent triangles are congruent.

12.

Statements

1. 2.

} M} MQQ

?i } N} NTT

3. 4.

} MTNT?M} M?T

QMT

5. 6.

n} MNNT?M} T?Q

n QMT

Reasons

1. Given 2. Given 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence 5. SAS Congruence Postulate 6. Corresponding parts of congruent triangles are congruent.

13.

Statements 1. A}B ? B}E

2. ADB ? ECB

3. ABD ? EBC

4. 5.

n} DBAB?D} C?B

n EBC

Reasons

1. Given 2. Given 3. Vertical Angles

Theorem 4. AAS Congruence Theorem 5. Corresponding parts of congruent triangles are congruent.

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