The Supplement Theorem | Exploring Angle Congruence and Supplementary Relationships in Geometry

supplements of congruent angles are congruent

The statement “supplements of congruent angles are congruent” refers to a property of angles known as the Supplement Theorem

The statement “supplements of congruent angles are congruent” refers to a property of angles known as the Supplement Theorem.

In geometry, angles that have the same measure are called congruent angles. Two angles are said to be supplements of each other if their measures add up to 180 degrees.

The Supplement Theorem states that if two angles are congruent, then their supplements will also be congruent. In other words, if angle A is congruent to angle B, and angle C is a supplement of angle A, then angle D, which is a supplement of angle B, will also be congruent to angle C.

Mathematically, this can be written as follows:
If ∠A ≅ ∠B, and ∠C is a supplement of ∠A, then ∠C ≅ ∠D

To illustrate this, let’s consider an example:
Suppose we have two angles, ∠A and ∠B, both measuring 60 degrees. Since they are congruent, we can say that ∠A ≅ ∠B.

Now, let’s find the supplements of these angles. Since the measures of ∠A and ∠B add up to 180 degrees, their supplements will also add up to 180 degrees.

If ∠A = 60 degrees, then its supplement ∠C will be 180 – 60 = 120 degrees. Similarly, if ∠B = 60 degrees, then its supplement ∠D will also be 180 – 60 = 120 degrees.

Therefore, by the Supplement Theorem, we can conclude that ∠C ≅ ∠D, or in this case, 120 degrees is congruent to 120 degrees.

This property is important in geometry and can be used to prove various geometric theorems and properties. It allows us to make deductions and draw conclusions based on the equality of angles and their supplements.

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