Is the following statement true? Why?
"Two quadrilaterals are similar,if their corresponding angles are equal".

In $\triangle ABC$,$AB = 24 \, cm$,$BC = 10 \, cm$,and $AC = 26 \, cm$. Is this triangle a right triangle? Give reasons for your answer.

Prove that the midpoints of the sides of any convex quadrilateral are the vertices of a parallelogram.

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 8$,$XZ = 6$ and $MZ = 4.8$,find $YZ$.

In $\Delta ABC$ and $\Delta DEF$,$\frac{AB}{DF} = \frac{BC}{EF}$ and $\angle B \cong \angle F$. Then,by $\ldots \ldots \ldots$ condition,the correspondence $ABC \leftrightarrow DFE$ is a similarity.

In $\Delta PQR$,$\overline{QM}$ is an altitude. If $PQ = 2PM$ and $RM = 3PM$,prove that $\Delta PQR$ is a right-angled triangle.