$∆\mathrm{ABC}$ and $∆\mathrm{X}\mathrm{Y}\mathrm{Z}$ are equilateral triangles and $\mathrm{A}\mathrm{B}=\mathrm{X}\mathrm{Y}$, state the conditions (s) under $∆\mathrm{A}\mathrm{BC}$ and $∆\mathrm{X}\mathrm{Y}\mathrm{Z}$ are congruent.

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.