In the figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a rhombus. Are $∆\mathrm{A}\mathrm{D}\mathrm{C}$ and $∆\mathrm{A}\mathrm{BC}$ congruent? What can you say $∆\mathrm{A}\mathrm{B}\mathrm{D}$ and $∆\mathrm{C}\mathrm{B}\mathrm{D}?$

In this figure, $\mathrm{T}\mathrm{S}\parallel \mathrm{P}\mathrm{Q}$ and $\mathrm{T}\mathrm{S}=\mathrm{P}\mathrm{Q}.$ Prove that the triangles $\mathrm{P}\mathrm{Q}\mathrm{R}$ and $\mathrm{S}\mathrm{T}\mathrm{R}$ are congruent.

In the figure, name the triangle which is congruent to $∆\mathrm{P}\mathrm{Q}\mathrm{R}$, keeping the letters in the right order. Give reasons.