Question

$△ABC$ is isosceles with AB = AC. Line segment AD bisects $\angle A$ and meets the base BC in D.
(i) Is $△ADB\cong △ADC?$
(ii) State the three pairs of matching parts used to answer (i).
(iii) Is it true to say that BD = DC?

Answer 1

(i) We have AB = AC (given)
$\angle BAD=\angle CAD\left(AD\text{bisects}\angle BAC\right)$
and AD = AD (common)
Therefore by SAS condition of congruence,$△ABD\cong △ACD.$
(ii) We have used
AB =AC; $\angle BAD=\angle CAD;AD=AD.$
(iii) Now $△ABD\cong △ACD$
therefore by c.p.c.t
BD = CD