Chapter 1.4, Problem 2PSA

To determine

To Prove: $\angle AGD\cong \angle EGB$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}\angle AGD\text{is a straight angle}\\ \angle EGB\text{is a straight angle}\end{array}$

Concept Used:

Two angles are said to be congruent if they are of the same measure.

Proof:

Here, we have

  $\begin{array}{l}\angle AGD\text{is a straight angle}\\ \Rightarrow m\angle AGD=180°\\ \angle EGB\text{is a straight angle}\\ \Rightarrow m\angle EGB=180°\\ \therefore m\angle AGD=m\angle EGB=180°\\ \Rightarrow \angle AGD\text{and }\angle EGB\text{are of the same measure, hence they are congruent}\text{.}\\ \therefore \angle AGD\cong \angle EGB\end{array}$