Question

In Figure, $AB=AD$ and $\angle BAC=\angle DAC$.

(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) $\angle ABC=$

(b) $\angle ACD=$

(c) Line segment AC bisects ….. And ……..

Answer 1

i) AB = AD (given)

$\angle BAC=\angle DAC\left(given\right)$

AC = CA (common)

Therefore by SAS condition of congruency, ΔABC ≅ ΔADC

ii) $\angle ABC=\angle ADC$ (corresponding parts of congruent triangles)

$\angle ACD=\angle ACB$ (corresponding parts of congruent triangles)

Line segment AC bisects $\angle Aand\angle C.$