What is $\angle \mathrm{A}$ in the triangle $\mathrm{ABC}$ ?

Identify the pairs of shapes which are similar and congruent and write the letter pairs.

In the figure, $\mathrm{DA}=\mathrm{DC}$ and $\mathrm{BA}=\mathrm{BC}$. Are the triangles $\mathrm{DBA}$ and $\mathrm{DBC}$ congruent? Why?

In the given figure, $\angle \mathrm{CIP}\equiv \angle \mathrm{COP}$ and $\angle \mathrm{HIP}\equiv \angle \mathrm{HOP}$. Prove that $\mathrm{IP}\equiv \mathrm{OP}$.

In the given figure, $\mathrm{AC}\cong \mathrm{AD}$ and $\angle \mathrm{CBD}\cong \angle \mathrm{DEC}.$ Prove that $△\mathrm{BCF}\cong △\mathrm{EDF}$

In the given figure, $△\mathrm{BCD}$ is isosceles with base $\mathrm{BD}$ and $\angle \mathrm{BAE}\equiv \angle \mathrm{DEA}$. Prove that $\mathrm{AB}\equiv \mathrm{ED}$.

In the given figure, $\mathrm{D}$ is the midpoint of $\mathrm{OE}$ and $\angle \mathrm{CDE}=90°.$ Prove that $△\mathrm{ODC}\cong △\mathrm{EDC}$.

Is $△\mathrm{PRQ}\cong △\mathrm{QSP}$ ? Why?