Question

Prove the following theorem: The acute angles of a right triangle are complementary.

Given: ΔABC with right angle C
Prove: ∠A and ∠B are complementary
How do you do a paragraph proof for this problem in 5 steps?

Answer 1

1. ∠C = 90° (given)

2. ∠A + ∠B + ∠C = 180° (Sum of ∠s in triangle)

3. ∠A + ∠B +90° = 180° (Substitution)

4. ∠A + ∠B = 90° (Algebra)

5. ∠A and ∠B are complementary (Def of complementary angles)

You could also construct an exterior angle from ∠C and prove it that way but that might be longer and more complicated.