Exercise 7.1

In the given figure, by which rule $△ABC\cong △DEF$?

If  ABCD is a parallelogram, then prove that $△ABD$ is congruent to $△CDB$.

$E \text{and} F$ are the midpoint of equal sides $AB \text{and} AC$ of a $△ABC$, respectively. Show that $BF=CE$.

In the given figure, $AB=BC$ and $AD=EC$. Show that $△ABE\cong △CBD$

In $△ABC$ and $△PQR$, if $AB=AC$, $\angle C=\angle P$ and $\angle B=\angle Q$, Prove that the two triangles are isosceles but not congruent.

In the adjoining figure, is an $PQR$ isosceles triangle with $PQ=PR, QS \text{and} RT$ are two medians of the triangle. Prove that  $QS=RT.$

In the adjoining figure, $AB=AC$ and $BE\text{ and} CF$ are bisectors of $\angle B \text{and} \angle C$, respectively. Prove that $△ECB\cong △FCB$.

In$△ ABC$and $△ PQR$, $\angle A = \angle Q$ and $\angle B= \angle R$. Which side of$△ PQR$ should be equal to side $BC$of $△ ABC$, so that the triangle two traingles are congruent.?