Congruent Complements Theorem
Congruent Complements Theorem states that if two angles are complements of congruent angles, meaning they add up to 90 degrees individually, then the two angles themselves are congruent.
Given:
- ∠A and ∠B are complements
- ∠A is congruent to ∠C
- ∠B is congruent to ∠D
To prove:
- ∠A is congruent to ∠C
- ∠B is congruent to ∠D
Proof of Congruent Complement Theorem
- ∠A + ∠B = 90∘ (Given: ∠A and ∠B are complements)
- Since ∠A is congruent to ∠C, we can substitute ∠C for ∠A: ∠C + ∠B = 90∘
- Similarly, since ∠B is congruent to ∠D, we can substitute ∠D for ∠B: ∠C + ∠D = 90∘
- Since the sum of angles ∠C and ∠D is also 90 degrees, and by the definition of complementary angles, angles ∠C and ∠D are also complements of each other.
- Therefore, by definition, angles ∠C and ∠D are congruent.
- Thus, ∠A is congruent to ∠C and ∠B is congruent to ∠D, as required.
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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