In the given figure $\mathrm{APB}$ and $\mathrm{CQD}$ are two congruent arcs. Prove that $\mathrm{AC}\parallel \mathrm{BD}$.

In the given figure, $\mathrm{ABC}$ is equilateral, $\mathrm{P}$and $\mathrm{S}$ are midpoints of arcs $\mathrm{AB}$ and $\mathrm{AC}$.

Prove that $\mathrm{PQ}=\mathrm{QR}=\mathrm{RS}$.

Give all the names that apply to this given figure.

In this given figure, $\mathrm{ABCD}$ is a rectangle. $\mathrm{P}$ is the midpoint of $\overline{\mathrm{AB}}$. Prove $△\mathrm{DPC}$ is isosceles.

In the given figure, $\mathrm{PQRS}$ is a rhombus with diagonal $\overline{\mathrm{PR}}$. $\mathrm{T}$ is any point on $\overline{\mathrm{PR}}$. Prove $\overline{\mathrm{TS}}=\overline{\mathrm{TQ}}$.

In the figure, $\mathrm{ABCD}$ is rhombus. Find $\mathrm{AB}$. (Express answer in mixed fraction)

In the figure,  $\mathrm{ABCD}$ is rhombus. Find $\mathrm{m}\angle \mathrm{ABC}$.