Question

$ABC$ and $DBC$ are two isosceles triangle on the same side of $BC$. Then, $\angle BDA=\angle CDA$.

• A. True
• B. False

Answer 1

The correct option is A True

Join AD.
In $△$ ABD and $△$ ACD,
$AB=AC$ (Given)
$BD=CD$ (Given)
$AD=AD$ (Common side)
$\therefore$ $△$ $ABD\cong △ACD$ (By SSS congruence rule)
Hence, $\angle BDA=\angle CDA$ (Corresponding angles of congruent triangles)