SOLUTION: Prove that if two angles are complements of the same angle, then the angles must be congruent. ( Use a paragraph proof ) Given: ∠ 1 and ∠ 2 are complementary. ∠ 2
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Question 463932: Prove that if two angles are complements of the same angle, then the angles must be congruent. ( Use a paragraph proof ) Given: ∠ 1 and ∠ 2 are complementary. ∠ 2 and ∠ 3 are complementary. Prove: ∠ 1 ≅ ∠ 3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
angle 1 is complement to angle 2
angle 2 is complement to angle 3
prove angle 1 is congruent to angle 3
angle 1 + angle 2 = 90 degrees (definition of complement)
angle 2 + angle 3 = 90 degrees (definition of complement)
angle 1 + angle 2 = angle 2 + angle 3 (substitution)
subtract angle 2 from both sides of the equation.
you are left with angle 1 = angle 3.
the geometric explanation is the subtraction property.
if a = b then a-c = b-c
the a was angle 1 + angle 2 = 90 degrees
the b was angle 2 + angle 3 = 90 degrees
the c was the subtraction of angle 2
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