Chapter 5.4, Problem 13PSB

Solution

To Prove: Each pair of consecutive angles in a parallelogram are supplementary.

Given information:

ABCD is a parallelogram.

Proof:

  

Here, $AB\parallel CD$

(Opposite sides of a parallelogram are parallel)

  $m\angle ABC+m\angle DCB={180}^{\circ }$

(Consecutive interior angles between two parallel lines)

Similarly, $AD\parallel BC$

(Opposite sides of a parallelogram are parallel)

  $m\angle BAD+m\angle CDA={180}^{\circ }$

(Consecutive interior angles between two parallel lines)