1. If the angles are congruent the measures are equal. That's the angle congruence postulate, usually too obvious to name.
2. The measures of complementary angles add to 90 degrees. 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. Angle 1 is congruent to Angle 3. Therefore Angles 1 and 3 are complementary.
