Question

$\text{In figure}AB=AD\text{and}\angle BAC=\angle DAC.$
(i) Identify the congruent triangles.
(ii) Find congruent parts for each of the following
$\text{(a)}\angle ABC$
$\text{(b)}\angle ACD$

Answer 1

i) AB = AD (given)
$\angle BAC=\angle DAC\text{(given)}$
AC = CA (common)
Therefore by SAS condition of congruency,
$△ABC\cong △ADC.$
(ii)
(a)$\angle ABC=\angle ADC\text{(c.p.c.t)}$
(b)$\angle ACD=\angle ACB\text{(c.p.c.t)}$