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 theorem in geometry. It states that if two angles are congruent, then their supplements are also congruent.
To understand this statement, we need to first define what we mean by supplement and congruent angles. Two angles are said to be congruent if they have the same measure. For example, two 45-degree angles are congruent because they both have the same measure of 45 degrees.
The supplement of an angle is another angle that, when added to the original angle, results in a total of 180 degrees. For example, the supplement of a 60-degree angle is a 120-degree angle, because 60 + 120 = 180 degrees.
Now, let’s prove the statement supplements of congruent angles are congruent:
Given: Angle A and angle B are congruent angles.
To Prove: Angle A’s supplement, angle C, is congruent to angle B’s supplement, angle D.
Proof:
Since angle A and angle B are congruent, we know that they have the same measure. Let’s call this measure x. So, mMore Answers:
Proven: The Congruence Of Alternate Exterior Angles Theorem.
The Corresponding Angles Postulate In Geometry: Solving Problems With Parallel Lines And Transversals
Complements Of Congruent Angles: Proof That Complementary Angles Are Congruent