Question

ΔABC and ΔDBC are two isosceles triangles on the same base BC (see figure). Show that ∠ ABD = ∠ ACD.

Answer 1

Given,
$△$ABC and BCD are isosceles triangle.
$\therefore$ AB = AC
BD = DC
Now,
Join point A and D with a line segment.
In ABD and ADC
AB = AC
BD = DC
AD = AD
$\therefore △ABD\cong △ADC$ by SSS Test.
$\angle ABD=\angle ACD$.... (CPCT)