Question

Given: g || h, 1||

Prove: 21 is supplementary to 16.

:: Corresponding angles postulate :: Congruent supplements theorem
:: Transitive property of equality :: vertical angle theorem
:: same side interior angle theorem

Answer 1

1. g||h, I||j (given)

2. ∠1 ≅ ∠3 ( vertical angle theorem)

3. ∠3 ≅ ∠11 (corresponding angles postulate)

4. ∠1 ≅ ∠11 (transitive property of equality)

5. ∠11 and ∠16 are supplementary (same side interior angle theorem)

6. ∠1 and ∠16 are supplementary (congruent supplements theorem)

What is a transversal?

A transversal is a line that intersects two or more other lines at distinct points.

When a transversal intersects two parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.

The angles are related as follows

1. g||h, i||j (given)

2. ∠1 ≅ ∠3 ( vertical angle theorem)

3. ∠3 ≅ ∠11 (corresponding angles postulate)

4. ∠1 ≅ ∠11 (transitive property of equality)

5. ∠11 and ∠16 are supplementary (same side interior angle theorem)

6. ∠1 and ∠16 are supplementary (congruent supplements theorem)

Complete question