Question

In triangle ABC, AB = AC and BD, CE are its two medians. Show that BD = CE.

Answer 1

Given that AB = AC and BD,CE are its two medians.

In $\Delta ABD$ and $\Delta ACE$,
AB = AC [given]
$\angle A=\angle A$ [common angle]
And AD = AE
$[\because AB=AC\Rightarrow \frac{1}{2}AB=\frac{1}{2}AC\Rightarrow AE=AD]$
As D is the mid-point of AC and E is the mid-point of AB,
$\therefore \Delta ABD\cong \Delta ACE$ [by SAS congruence rule]
$\Rightarrow BD=CE$ [by CPCT]