Question

Write a two-column proof for the following conjuncture. You may not need to use all of the rows of the two-column table provided below. You may also add additional rows if needed given parallelogram ABCD

(Given 7 Columns on Assignment)

Prove: angle A and angle B are supplementary
Angle B and angle C are supplementary.​

Answer 1

For any parallelogram, each two opposite sides are parallel and equal.

So, for the given ABCD be a parallelogram

AB // CD and CB is a transversal.

Because of the sum of the interior angles on the same side of the transversal is 180°

So, ∠B + ∠C = 180°

∴ Angle B and angle C are supplementary.

And

AD // BC and AB is a transversal.

Because of the sum of the interior angles on the same side of the transversal is 180°

So, ∠A + ∠B = 180°

∴ Angle A and angle B are supplementary.