Alternate Angles Theorem
Alternate Angles Theorem, also known as the Alternate Interior Angles Theorem, states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Proof of Alternate Angles Theorem
The proof of alternate angles theorem is discussed below:
To prove this theorem, let’s consider two parallel lines, ℓ1 and ℓ2, intersected by a transversal line, t, as shown below:
∠3 and ∠5 be alternate interior angles formed by the transversal t intersecting lines ℓ1 and ℓ2.
Now, from Corresponding Angle Theorem,
∠1 = ∠5 (Corresponding Angles)…..(i)
Now, from Vertical Angle Theorem,
∠1 = ∠3 (Vertical Angles)…..(ii)
Hence, from equations (i) and (ii)
∠3 = ∠5
Hence, alternate angles ∠3 and ∠5 are corresponding to each other.
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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