Table of Contents
- Converse of Alternate Angles Test
- Summary
- What’s Next?
In the previous segment, we learnt about the Alternate angles test and proved it as well. In this segment, we will prove the converse of this test.
What is the Converse of the alternate angles test?
The converse of alternate angles test states that if 2 lines are parallel, then the alternate angles formed by a transversal are congruent.
Given: lines AB and CD are parallel to each other.
Fig 1
To Prove:
∠AGH ≅ ∠GHD
We use indirect proof to prove this. That is, assume that alternate angles ∠AGH and ∠GHD are not congruent.
For this, draw a line JK such that the alternate interior angles ∠JGH and ∠GHD are equal as shown below.