Question

In Fig. 31, AB = AD and ∠BAC = ∠DAC.
(i) State in symbolic form the congruence of two triangles ABC and ADC that is true.
(ii) Complete each of the following, so as to make it true:
(a) ∠ABC = ........
(b) ∠ACD = ........
(c) Line segment AC bisects ..... and .....

Answer 1

i) AB = AD (given)
$\angle BAC=\angle DAC$ (given)
AC = CA (common)
Therefore by SAS conditionof congruency, $△ABC\cong △ADC$.

ii) $\angle ABC=\angle ADC$ (c.p.c.t)
$\angle ACD=\angle ACB$ (c.p.c.t)