Complements Of Congruent Angles: Proof That Complementary Angles Are Congruent

complements of congruent angles are congruent

Complements of congruent angles are congruent

Complements of congruent angles are also congruent.

Let’s begin by defining what we mean by complement and congruent.

Complementary angles are two angles that add up to 90 degrees.

Congruent angles are two angles that have the same measure.

Now, let’s suppose we have two congruent angles, let’s call them angle A and angle B. If angle A is complementary to angle C and angle B is complementary to angle D, then we know:

– Angle A + angle C = 90 degrees (definition of complementary angles)
– Angle B + angle D = 90 degrees (definition of complementary angles)

We can rearrange these two equations and substitute angle A = angle B (since they are congruent):

– Angle A = 90 degrees – angle C
– Angle B = 90 degrees – angle D

Now, we want to prove that these two angles are also congruent:

– Angle A = angle B (given that they are congruent)
– 90 degrees – angle C = 90 degrees – angle D (using the previous equation)
– – angle C = – angle D (subtracting 90 degrees from both sides)
– angle C = angle D (multiplying both sides by -1 and changing the sign)

Therefore, we have shown that if angle A and angle B are congruent and complementary to angles C and D respectively, then angles C and D are also congruent. Hence, complements of congruent angles are congruent.

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