Chapter 4.2, Problem 13WE

To determine

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

Answer to Problem 13WE

  $\Delta ABC\cong \Delta AFC$ by SAS postulates.

Explanation of Solution

Given information :

The given figure is,

From figure it is seen that $BC\left|\right|AF$ and AC is a transversal line.

So $\angle BCA=\angle CAF\left(Alternate\mathrm{int}eriorangle\right)$

Now, in $\Delta ABCand\Delta AFC$

  $\begin{array}{l}AC=AC\left(commonside\right)\\ AB=AF\end{array}$

Therefore, by SAS postulates $\Delta ABC\cong \Delta AFC$