Chapter 5.2, Problem 13PSA

To determine

To Prove: $\overline{AT}\parallel \overline{GO}$ .

Explanation of Solution

Given:

  

  $\angle FAT\cong \angle HOG$

Concept Used:

When parallel lines is intersected by a transversal alternate exterior angles are equal.

Proof:

Here, we have

  

As we extend lines TA and GO, we get two alternate exterior angles $\angle FAT\text{and}\angle HOG$ such that

  $\begin{array}{l}\angle FAT\cong \angle HOG\\ \text{Since, we know that when parallel lines is intersected by a transversal alternate exterior angles are equal}\text{.}\\ \Rightarrow \overline{AT}\parallel \overline{GO}\text{with transversal }\overline{AO}\end{array}$