Question

Write a two-column proof for the following conjecture.

Given: Parallelogram ABCD
Prove: ∠A and ∠B are supplementary.
∠B and ∠C are supplementary.

Answer 1

this is how we were asked to do it. Different teachers ask for different reasons . Hope this helps!

Answer 2

Explanation:

Given: ABCD is a parallelogram

To prove: ∠A and ∠B are supplementary,∠B and ∠C are supplementary.

Proof:

Statement Reason

1. Quadrilateral ABCD is a parallelogram Given

2. AB||DC and AD||BC Opposite sides of parallelogram are parallel

3. ∠A and ∠B are same side interior angles

and ∠B and ∠C are same side interior angles. Definition of parallelogram

4. m∠A+m∠B=180°

and m∠B+m∠C=180° Same side angles of a parallelogram are of 180°

5. ∠A and ∠B are supplementary.

and ∠B and ∠C are supplementary. Definition of supplementary angles.