Step 1: draw a right triangle. label the acute angles as angles a and b. label the right angle as angle c. step 2: prove the acute angles of a right triangle are complementary. given: triangle abc with angle c a right angle prove: angle a and angle b are complementary

1)The sum of the angles A B C is 180 degrees (a line). Reason: All triangles have this property.
2) 2 right angles are supplementary (add up to a line). Reason: If we have a normal to a line, the two resulting angles are right and they add up to a line.
3) A is supplementary to the sum of B and C. Reason: 1)
4) A right angle is supplementary to A. Reason: 2)
5) The sum of B and C is a right angle. Hence, B and C are complimentary. Reason: This results from 3 and 4 and congruency of angles.