Question

Question 1
ABC is an isosceles triangle with AB = AC and BD, CE are its two medians. Show that BD = CE.

Answer 1

$\Delta ABC$ is an isosceles triangle in which AB=AC and BD,CE are its two medians.

In $\Delta ABC$ 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,
$\therefore \Delta ABC\cong \Delta ACE$ [by SAS congruence rule]
$\Rightarrow BD=CE$ [by CPCT]