Question

$△ABC$ and $△DBC$ are two isosceles triangles on the same base BC (see the given figure). Then, $\angle ABD$ = _______.

• A. $\angle BCA$
• B. $\angle CDB$
• C. $\angle ABC$
• D. $\angle ACD$

Answer 1

The correct option is D $\angle ACD$


Join $AD$.
In $△ABD$ and $△ACD$,
$AB=AC$ (given)
$BD=CD$ (given)
$AD=AD$ (common side)
$\therefore △ABD\cong △ACD$ (by SSS congruence rule)
$\Rightarrow \angle ABD=\angle ACD$ (by CPCT)