Complementary Angles Explanation: Understanding Congruency through Complementary Angles

If two angles are complementary to the same angle, then

they are congruent

they are congruent.

To understand this concept, let’s first define what it means for angles to be complementary. Two angles are said to be complementary if the sum of their measures is 90 degrees.

Now, let’s consider two angles, let’s call them angle A and angle B, that are both complementary to angle C.

This means that the measure of angle A + the measure of angle C = 90 degrees, and the measure of angle B + the measure of angle C = 90 degrees.

Now, let’s compare angle A and angle B. We can subtract the measure of angle C from both sides of the equation for angle A to get:

(measure of angle A + measure of angle C) – measure of angle C = 90 degrees – measure of angle C
measure of angle A = 90 degrees – measure of angle C

Similarly, for angle B, we can subtract the measure of angle C from both sides of the equation to get:

measure of angle B = 90 degrees – measure of angle C

Now, if we compare the measures of angle A and angle B, we can see that they are both equal to (90 degrees – measure of angle C).

Since the expression (90 degrees – measure of angle C) is the same for both angles A and B, this means that angle A and angle B have the same measure and are therefore congruent.

Therefore, if two angles are complementary to the same angle, then they are congruent.

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