hw-3b-iii-solns - HW #3 B, Part III Solutions M 333L FALL...

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HW #3 B, Part III Solutions M 333L FALL 2010 Theorem 3.2.3 (Restated for clarity) Prove parts (2) and (4). ( 1 ) Supplements of congruent angles are congruent. ( 2 ) Complements of congruent angles are congruent. ( 3 ) Supplements of the same angle are congruent. ( 4 ) Complements of the same angle are congruent. Proof of (2): Let ,, ABC DEF PQR and XYZ be any four angles such that is a complement of PQR and DEF is a complement of and PQR   . [ We need to prove that   . ] By definition of “complement,”   m ABC +   m PQR = 90° , so   m ABC = 90°   m PQR , and   m DEF +   m = 90° , so   m DEF = 90°   m . By definition of “congruent,”   m PQR =   m . By substitution,   m ABC = 90°   m .   m ABC =   m DEF
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This note was uploaded on 11/02/2010 for the course M Modern Geo taught by Professor Shirley during the Spring '10 term at University of Texas at Austin.

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