Table of Contents
Table of Contents
- Alternate Angles Test
- Summary
- What’s Next?
In the previous segment, we learnt about the different angles formed by a transversal and parallel lines. In this segment, we will understand the Alternate angles test.
What is the Alternate angles test?
The alternate angles test states that if a pair of alternate interior angles formed by a transversal of two coplanar lines are congruent, then the two lines are parallel.
Given:
Two coplanar lines AB and CD and transversal EF meeting the lines are points G and H respectively.
Fig 1
∠AGH and ∠GHD are alternate angles.
To Prove: line AB || line CD
We use indirect proof to prove the alternate angles test. That is, we assume that lines AB and CD intersect each other. If this assumption is proved wrong, then it means that lines AB and CD are parallel.
For this, redraw the lines AB and CD to meet at point Z forming △GZH as shown in the figure
below.
