Question

If a transversal intersects two parallel lines, then interior angles on the same side of the
transversal are
​

Answer 1

Answer:

Definition

Angles on the same side of the transversal are angles that are in one of the half-planes formed by the transversal.

Usually this term is combined with interior or exterior angles to define "interior angles on the same side of the transversal" and "exterior angles on the same side of the transversal".

Examples

In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are interior angles on the same side of the transversal:

angleA and angleF

angleD and angleG

Download video: MP4 (162 KB)

In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are exterior angles on the same side of the transversal:

angleB and angleE

angleC and angleH

Download video: MP4 (163 KB)

Theorem

When a transversal intersects two lines, the two lines are parallel if and only if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary (sum to 180°).

In illustration one of the example section above, LINE 1 and LINE 2 are parallel and both interior and exterior angles on the same side of the transversal are supplementary.

In illustration two of the example section above, LINE 1 and LINE 2 are NOT parallel and both interior and exterior angles on the same side of the transversal are NOT supplementary.