Congruent Supplements Theorem
Congruent Supplements Theorem states that if two angles are supplements of congruent angles, then the two angles are congruent. In simpler terms, if two angles add up to 180 degrees and those angles they add up to are congruent, then the two angles themselves are congruent.
Proof of Congruent Supplement Theorem
The proof of congruent supplement theorem is explained below:
Let’s consider two angles, angle A and angle B, which are supplements of congruent angles angle X and angle Y, respectively.
Given: ∠A and ∠B are supplements, and ∠X ≅ ∠Y (congruent angles).
- We know that the sum of the measures of supplementary angles is 180 degrees.
- So, we have: ∠A + ∠X = 180° and ∠B + ∠Y = 180°.
- Since ∠X ≅ ∠Y, we can substitute ∠X for ∠Y in the equation: ∠B + ∠X = 180°.
- Now, from step 4, we have: ∠A + ∠X = 180° and ∠B + ∠X = 180°.
- Subtracting ∠X from both sides of the equations, we get: ∠A = ∠B.
- Thus, we have proven that if ∠A and ∠B are supplements of congruent angles ∠X and ∠Y, respectively, then ∠A ≅ ∠B.
Congruent Angles
Congruent angles are angles that have equal measure. Thus, all the angles in the geometry that have sam measure are called congruent angles.
In this article, we will understand the meaning of congruent angles, their properties, the congruent angles theorem, the vertical angles theorem, the corresponding angles theorem, and the alternate angles theorem.
Table of Content
- What are Congruent Angles?
- Congruent Angles Theorem
- Vertical Angles Theorem
- Corresponding Angles Theorem
- Alternate Angles Theorem
- Congruent Supplements Theorem
- Congruent Complements Theorem
- How to Find Congruent Angles
- Constructing Congruent Angles
- Construction of a Congruent Angle to the Given Angle
- Construction of Two Congruent Angles
- Congruent Angles Properties
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