Question

$ABC$ and $DBC$ are two isosceles triangle on the same side of $BC$. Then, $DA$ (or $AD$) produced bisects $BC$ at right angle.
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Join AD.Let it meet BC in O
In $△$ ABO and $△$ ACO,
AB = AC (Given)
$\angle ABO=\angle ACO$ (ABD is an isosceles tiangle)
AO = AO (Common side)
$\therefore$ $△ABO\cong △ACO$ (By SSA congruence rule)
Hence, $\angle AOB=\angle AOC=x$ (Corresponding angles of congruent triangles)
Now, $\angle AOB+\angle AOC=180$
$x+x=180$
$x=90$
Thus, AD bisects BC at right angles.