Q). In the adjoining figure, AB = AC and D is mid-point of BC. Use SSS rule of congruency to show that

(i). $△ABD\cong △ACD$
(ii). AD is bisector $\angle A$.
(iii). AD is perpendicular to BC.

In triangle ABD and triangle ACD,
AB=AC [Given]
BD=CD[D is the mid point of BC]
AD=AD[Common ]
By SSS congruence criterion,
/\ABD=/\ACD
​Now we have to prove that angle BAD=CAD
Since we have proved triangle ABD and triangle ACD congruent their corresponding parts will also be equal.....
So, angle BAD=angle CAD
Similarly, angle ADB=angle ADC [cpct]