Chapter 3, Problem 16CR

To determine

To Prove: The segments drawn from the mid-point of the base of an isosceles triangle to the mid-points of the legs are congruent.

Explanation of Solution

Given information: $\Delta ABC$ is an isosceles triangle is provided in the question which will help

to find the solution.

  

Proof: In $\Delta DEB$ and $\Delta FEC$

  $\angle B=\angle C$ (opposite angles of equal sides)

DB = FC (Isosceles triangle)

BE = EC (as E is mid-point)

So, $\Delta DEB\cong \Delta FEC$ (by Side angle side congruency rule)

Hence, DE = FE (by corresponding parts of congruent triangles)