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hw-3b-iii-solns

# 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 ABC is a complement of PQR and DEF is a complement of XYZ and PQR XYZ   . [ We need to prove that ABC DEF   . ] By definition of “complement,” m ABC + m PQR = 90° , so m ABC = 90° m PQR , and m DEF + m XYZ = 90° , so m DEF = 90° m XYZ . By definition of “congruent,” m PQR = m XYZ . By substitution, m ABC = 90° m XYZ . m ABC =
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