Chapter 3.4, Problem 4PSA

To determine

To prove that $\overline{FD}$ is a median.

Explanation of Solution

Given information : In this question, we have given that $\angle CFD\cong \angle EFD$ and $\overline{FD}$ is altitude.

Formula used: SAS Congruency rule.

Proof: As, $\overline{FD}$ is altitude,

  $\therefore \angle FDC\cong \angle FDE$

Now, In $\Delta FDC$ and $\Delta FDE$ ,

  $\angle FDC\cong \angle FDE$ (Proved above)

  $\overline{FD}\cong \overline{FD}$ (Common)

  $\angle CFD\cong \angle EFD$ (Given)

  $\therefore \Delta FDC\cong \Delta FDE$ (BY SAS Congruency rule)

  $\therefore \Delta FDC\cong \Delta FDE$ (BY CPCT)

  $\therefore$ $\overline{FD}$ is a median.