Check whether the following pairs of triangles are congruent. If they are congruent, state the congruence criterion.

 

Check whether the following pairs of triangles are congruent. If they are congruent, state the congruence criterion.

Check whether the following pairs of triangles are congruent. If they are congruent, state the congruence criterion.

Check whether the following pairs of triangles are congruent. If they are congruent, state the congruence criterion.

In the given figure, $\mathrm{AB}=\mathrm{CD}$ and $\mathrm{AD}=\mathrm{BC}$. Prove that $\angle \mathrm{BAC}=\angle \mathrm{ACD}$.

In the given figure, $\mathrm{AB}=\mathrm{DE}, \mathrm{AC}=\mathrm{DF} \text{and} \mathrm{BF}=\mathrm{CE}$. Are the two triangles congruent?

In the given figure, $\mathrm{AD}=\mathrm{BC}$ and $\angle \mathrm{ADC}=\angle \mathrm{BCD}$. Prove that $\mathrm{AC}=\mathrm{BD}$.

In the given figure, $\mathrm{ABCD}$ is a rectangle and $\mathrm{AP}=\mathrm{DQ}$ and $\mathrm{AR}=\mathrm{PD}$. Prove that $\mathrm{PQ}=\mathrm{PR}$.

In the given figure, $\mathrm{QR}=\mathrm{RS}, \mathrm{PQ}=\mathrm{TS} \text{and} \angle \mathrm{Q}=\angle \mathrm{S}$. Prove that $\mathrm{PR}=\mathrm{TR}$.