Chapter 4.2, Problem 9WE

To determine

Whether the $\Delta ABC$ is congruent to another triangle by SSS, SAS, or ASA postulates.

Answer to Problem 9WE

No congruence can be deduced.

Explanation of Solution

Given information :

The given figure is,

From the given figure it is clear that in both the triangles $\Delta ABCand\Delta AGC$

  $\begin{array}{c}\angle ACB={180}^{°}-\left({59}^{°}+{60}^{°}\right)\\ ={180}^{°}-{119}^{°}\\ ={60}^{°}\end{array}$

And

  $\begin{array}{c}\angle CAG={180}^{°}-\left({61}^{°}+{60}^{°}\right)\\ ={180}^{°}-{121}^{°}\\ ={59}^{°}\end{array}$

Now, we have two triangles $\Delta ABCand\Delta AGC$ having corresponding angles are equal.

But that doesn’t guarantee that the triangles are congruent.

Triangles may be similar.

Therefore, no congruence can be deduced.