supplements of congruent angles are congruent
If two angles are supplementary to two the same angle then they are congruent.
The statement supplements of congruent angles are congruent is a true statement in Euclidean geometry.
Two angles are congruent if they have the same measure. Two angles are supplements of each other if the sum of their measures is 180 degrees. For example, angles of 60 degrees and 120 degrees are supplements of each other.
Let’s say we have two congruent angles, angle A and angle B. Then we can say that:
A = B
Now, if we take the supplements of these two angles, we get:
180 – A = supplement of angle A
180 – B = supplement of angle B
By substituting A = B, we get:
180 – A = 180 – B
This can be simplified as:
supplement of angle A = supplement of angle B
Therefore, we can say that supplements of congruent angles are congruent. This property is useful in solving problems involving angles, such as finding the measures of angles in geometric shapes.
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