Question

In the isosceles $△ABC,AB=AC$. Perpendiculars $AD$ and $CE$ are rawn from the vertices $B$ and $C$ to the opposite sides. Show that $BD=CE$.

Answer 1

Given AB$=$AC

Also, BD and CE are two medians.

Hence, E is the midpoint of AB and D is the midpoint of CE.

Hence $=\frac{1}{2}AB=\frac{1}{2}AC$

$BE=CD$ (given)

In $\Delta BEC$ and $\Delta CDB$, $BE=CD$(given)

$\angle EBC=\angle DCB$(angles opposite to equal sides AB and AC)

$BC=CB$(common)

Hence $\Delta BEC\cong \Delta CDB$(by SAS)

$BD=CE$ (by CPCT)

Hence proved.