1. If the angles are congruent the measures are equal. Â That's the angle congruence postulate, usually too obvious to name.
2. The measures of complementary angles add to 90 degrees. Â That's the definition of complementary angles.
3. We substitute m∠2 for m∠1 so now m∠2 + m∠3 = 90 degrees.
4. The measures add to 90 degrees so now we conclude ∠2 and ∠3 are complementary.
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Why did this proof bother with the measures at all? Proof: Angles 2 and 3 are complementary. Â Angle 1 is congruent to Angle 3. Â Therefore Angles 1 and 3 are complementary.