Question

In $△ABC$, AD is perpendicular bisector of BC (See adjacent figure). Show that $△ABC$ is an isosceles triangle in which $AB=AC$

Answer 1

Given: $AD$ is the perpendicular bisector of $BC$.

To Prove:$△ABC$ is an isosceles triangle. i.e,$AB=AC$

Proof: In $△ADB$ and $\triangle{ADC},

$AD=AD$(Common)

$△ADB=△ADC$. ( each ${90}^{\circ }$)

$\Rightarrow BD=CD$

where $AD$ is the perpendicular bisector

Therefore, $△ADB\cong △ADC$ ( by SAS congruence rule)

$\Rightarrow AB=AC$ (by CPCT)

So,$△ABC$ is an isosceles triangle.

Note: In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.