$PQRS$ is a parallelogram. If the two diagonals are equal,find the measure of $\angle PQR$. (in $^{\circ}$)

It is given that $\triangle ABC \cong \triangle FDE$. If $AB = 5 \, cm$,$\angle B = 40^{\circ}$,and $\angle A = 80^{\circ}$,then which of the following is true?

$CDE$ is an equilateral triangle formed on side $CD$ of a square $ABCD$ (see figure). Show that $\triangle ADE \cong \triangle BCE$.

If $\triangle ABC \cong \triangle PQR$ and $\triangle ABC$ is not congruent to $\triangle RPQ$,then which of the following is not true?

In the given figure,$AB = AC$ and $BP = CQ$. Prove that $\Delta APQ$ is an isosceles triangle.

In triangles $ABC$ and $PQR$,$\angle A = \angle Q$ and $\angle B = \angle R$. Which side of $\triangle PQR$ should be equal to side $BC$ of $\triangle ABC$ so that the two triangles are congruent? Give reason for your answer.