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 ,,ABCDEFPQR andXYZbe any four angles such that ABCis a complement of PQRand DEFis a complement of XYZand PQRXYZ . [ We need to prove that ABCDEF . ] By definition of “complement,” mABC+ mPQR= 90° , so mABC= 90° –mPQR, and mDEF+ mXYZ= 90° , so mDEF= 90° –mXYZ. By definition of “congruent,” mPQR= mXYZ. By substitution, mABC= 90° –mXYZ. mABC=
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