Understanding the Supplementary Angles Theorem | A Key Concept in Angle Congruence and Geometry

Name the theorem: If two angles are supplements of the same angle (or of congruent angles) then the two angles are congruent.

The theorem which states that if two angles are supplements of the same angle or congruent angles, then the two angles are congruent is called the Supplementary Angles Theorem

The theorem which states that if two angles are supplements of the same angle or congruent angles, then the two angles are congruent is called the Supplementary Angles Theorem.

Supplementary angles are a pair of angles that add up to 180 degrees. This theorem basically says that if two angles each independently supplement the same angle or are congruent to each other, then they must also be congruent to each other.

To illustrate this, let’s assume angle A and angle B are both supplements of angle X. This means that angle A + angle X = 180 degrees, and angle B + angle X = 180 degrees.

Now, we need to prove that angle A and angle B are congruent. Since angle A + angle X = 180 degrees and angle B + angle X = 180 degrees, we can subtract angle X from both equations:

angle A = 180 degrees – angle X
angle B = 180 degrees – angle X

From these equations, we can see that both angle A and angle B will have the same value, as they are both equal to 180 degrees minus angle X. Therefore, angle A and angle B are congruent.

This theorem can also be extended to apply to congruent angles. If angle A and angle B are congruent to angle X, meaning they have the same measure as angle X, then angle A and angle B will also be congruent to each other.

Overall, the Supplementary Angles Theorem is a fundamental concept in geometry that helps in proving and understanding the congruence of angles.

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