Chapter 5.1, Problem 32WE

To determine

To proof: Side AB is equal to angle CE .

Explanation of Solution

Given:

The parallelogram is shown below:

  

ABCD is a parallelogram. Angle A is equal to E .

Calculation:

Line segment AB is parallel to line CD as ABCD is parallelogram.

  $\angle A=\angle D\left(\text{Corresponding}\text{angle}\right)\mathrm{......}\left(1\right)$

In triangle CDE , side CD is equal to CE .

  $\angle A=\angle E\left(\text{Given}\right)\mathrm{......}\left(2\right)$

Thus, from equations (1) and (2),

  $\angle D=\angle E$

And,

  $CE=CD\left(\text{Sides}\text{opposite}\text{to}\text{}\text{equal}\text{}\text{angles}\right)\mathrm{......}\left(3\right)$

As ABCD is parallelogram then,

  $AB=CD\mathrm{......}\left(4\right)$

Thus, from equations (3) and (4),

  $AB=CE$

Hence, this proves that the side AB is equal to angle CE .