Chapter 4.7, Problem 22WE

To determine

To prove: The medians drawn to the legs of an isosceles triangle are congruent using

two-column method.

Explanation of Solution

Given:

An isosceles triangle with medians drawn to the legs.

The isosceles triangle with median drawn to the legs is shown below,

  

Here, BD and CE are medians of triangle ABC.

Statement :	Reason:
$\overline{AB}\cong \overline{AC}$	$\Delta ABC$ is an isosceles.
$\angle ABC\cong \angle ACB$	Using isosceles theorem.
$\angle \overline{BE}\cong \angle \overline{CD}$	$BE=\frac{1}{2}AB;CD=\frac{1}{2}AC$
$\overline{BC}\cong \overline{BC}$	Reflexive property.
$\Delta BEC\cong \Delta CDB$	SAS postulate
$\overline{CE}\cong \overline{BD}$	Corresponding parts of congruent triangle are congruent
$\overline{BD}\cong \overline{CE}$	Hence proved.