Sign In
Consider a pair of lines cut by a transversal. The pairs of exterior angles with different vertices that lie on the same side of the transversal are called same-side exterior angles or co-exterior angles.
In the diagram, two pairs of same-side exterior angles can be identified. Pair1: & ∠ 1 and ∠ 8 Pair2: & ∠ 2 and ∠ 7 If two parallel lines are cut by a transversal, then the same-side exterior angles are supplementary. The same logic in reverse can be applied. If two lines and a transversal form same-side exterior angles that are supplementary, then the lines are parallel.
| If | Then |
|---|---|
| l_1 ∥ l_2 | m ∠ 1+m ∠ 8=180^(∘) and m ∠ 2 + m ∠ 7 = 180^(∘) |
| m ∠ 1+m ∠ 8=180^(∘) or m ∠ 2 + m ∠ 7 = 180^(∘) | l_1 ∥ l_2 |
These statements are supported by the Same-Side Exterior Angles Theorem and its converse.