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Yes, the corresponding triangle sides are congruent } } } } } } } } } } } } 6. No; JK À MP, JL À MN 7. 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M*+,zzM-,+zz ] ] *,z-+z ] ] 02/6%*+z-,z 'EOMETRY #HAPTER2ESOURCE"OOK Answer Key Lesson 4.4 Study Guide 1. Yes; You are given that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. 2. Yes; ∠ JKN and ∠ MKL are congruent because they are vertical angles. So you have two sides and the included angle of one triangle that are congruent to two sides and the included angle of another triangle. 3. No; You have two sides in nWXY that are congruent to two sides in n ZXY, but the angle in n ZXY is not the included angle. 4. Statements } } H 1. AB > DB } } 2. BC ⊥ AD 3. ∠ ACB and ∠ DCB are right angles. 4. n ABC and n DCB are right triangles. } } L 5. BC > BC 6. n ABC > n DBC Reasons 1. Given 2. Given 3. Def. of ⊥ lines 4. Def. of a right triangle 5. Reflexive Property of Congruence 6. HL Congruence Theorem 5. Statements 1. ∠ JKL and ∠ MLK are right angles. 2. n JKL and n MLK are right triangles. } } 3. JL > MK } } 4. KL > LK 5. n JKL > n MLK } } 6. JK > ML Reasons 1. Given 2. Def. of a right triangle 3. Given 4. Reflexive Property of Congruence 5. HL Congruence Theorem 6. 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'"#"{ z{'! z 02/6%Ng'#!Ng"!# ] ] z{'! z #"{ "#!'!# 'IVEN '" !LTERNATE)NTERIOR N'#!N"!# 'IVEN !!3#ONGRUENCE4HEOREM ] ] !#z!#z 2EmEXIVE0ROPERTY ÝiÀVÃiÃÊvÀÊÝ>«iÊÓ 7ÀÌiÊ>ÊyÊÜÊ«ÀvÊÌÊà ÜÊÌ >ÌÊÌ iÊÌÀ>}iÃÊ>ÀiÊV}ÀÕiÌ° {° ')6%.013213 130132 02/6%N013N213 'EOMETRY #HAPTER2ESOURCE"OOK ,-/*./ 02/6%Ng-*.Ng., x° ')6%./-./.- #OPYRIGHT¥BY-C$OUGAL,ITTELLADIVISIONOF(OUGHTON-IFmIN#OMPANY --" Ê{°x £° Answer Key Lesson 4.5 Study Guide 1. The vertical angles are congruent, so two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. 2. Two pairs of angles and a non-included pair of sides are congruent. The triangles are congruent by the AAS Congruence Theorem. 3. Two pairs of sides and a pair of angles are congruent. 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If you can show that n JKM > n LKM, then you will know that JK > LK. Since KM > KM by the reflexive property, then n JKM > n LKM by the SAS Congruence Postulate. Because corresponding parts of } } congruent triangles are congruent, JK > LK. 2. If you can show that n PQR > n RST, then you will know that ∠ RPQ > ∠ TRS. Because RQ i TS, ∠ PRQ > ∠ RTS by the Corresponding Angles Postulate. By the AAS Congruence Theorem, n PQR > n RST. Because corresponding parts of congruent triangles are congruent, ∠ RPQ > ∠ TRS. 3. Use the SAS Congruence Postulate to prove that n ABF > n EBC. Then state that ∠ AFB > ∠ ECB because they are corresponding parts of congruent triangles. ∠ CBD and ∠ FBG are congruent because they are vertical } } angles. Use the ASA Congruence Postulate to prove that BG > BD. } } 4. Use the SAS Congruence Postulate to prove that n PTS > n PRS. Then state that PT > PR because they are corresponding parts of congruent triangles. 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From part (b) you know that n ACD is equiangular. By the Corollary to the Converse of Base Angles } } } } } Theorem, n ACD is equilateral, and AD > AC. Because BC > ED, then BC 1 CD 5 ED 1 DC, and BD 5 } EC. Therefore, n ABD > n AEC by the SSS Congruence Postulate.