How To Prove That Complements Of Congruent Angles Are Congruent – A Math Explanation

complements of congruent angles are congruent

Complements of congruent angles are congruent

To understand why complements of congruent angles are congruent, we need to first understand what we mean by congruent angles and complementary angles.

Congruent angles are angles that have the same measure. This means that if you were to measure the size of two congruent angles, you would get the same result. For example, if angle A has a measure of 60 degrees, and angle B also has a measure of 60 degrees, then angle A and angle B are congruent.

Complementary angles are two angles that add up to 90 degrees. This means that if you were to add the measure of two complementary angles, you would get 90 degrees. For example, if angle C has a measure of 30 degrees, then its complement (angle D) would have a measure of 60 degrees, because 30 + 60 = 90.

Now, if we have two congruent angles that are complementary, this means that they have the same measure and their sum is 90 degrees. Let’s call these angles E and F. We know that E and F are congruent, so they have the same measure. We also know that they are complementary, so their sum is 90 degrees.

Since E and F have the same measure, we can replace one of the angles with the other in the equation that represents their sum. This means that we can say 2E = 90, which simplifies to E = 45. Since E and F are congruent, we know that F must also have a measure of 45 degrees.

Therefore, we can conclude that complements of congruent angles are congruent. In this case, since angles E and F have the same measure and are complementary, they are congruent.

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