Question

Explain how you would prove the following. Given that $\overline{HY}\cong \overline{LY},\overline{WH}\left|\right|\overline{LF}$. Prove that $\Delta WHY\cong \Delta FLY$.

Short answer

$\mathit{\Delta }\mathit{W}\mathit{H}\mathit{Y}\mathbf{\cong }\mathit{\Delta }\mathit{F}\mathit{L}\mathit{Y}$

Step-by-step solution

Step 1. Consider the figure.

Consider the figure.

Step 2. Step description.

Use the two-column proof as follows:

Statement	Reasons
$\overline{HY}=\overline{LY}$	From the question.
$\angle HYL=\angle FYL$	Vertical angles are equal.
$\angle H=\angle L$	Alternate interior angles
$\Delta WHY\cong \Delta FLY$	By Angle-side-angle Postulate

Step 3. Step description.

Therefore, $\Delta WHY\cong \Delta FLY$.