In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XY = 5.6$,$XP = 1.4$ and $XZ = 7.2$,find $XQ$.

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ : PR = 5 : 4$ and $SR = 5.6 \text{ cm}$,then $QR = \ldots \text{ cm}$.

In $\Delta ABC$,$\overline{AD}$ is a median. The bisectors of $\angle ADB$ and $\angle ADC$ intersect $\overline{AB}$ and $\overline{AC}$ at $E$ and $F$ respectively. Prove that $\overline{EF} \parallel \overline{BC}$.

In $\Delta PQR$,$m \angle P = 90^{\circ}$ and $\overline{PM}$ is an altitude. If $QM = 2x^{2}$ and $RM = 8x^{2}$,then $PM = \ldots \ldots$

In $\Delta ABC,$ the midpoints of the sides are $P, Q, R.$ In $\Delta PQR,$ the midpoints of the sides are $X, Y, Z.$ If the area of $\Delta XYZ$ is $20,$ find the area of $\Delta PQR$ and $\Delta ABC.$

In $\Delta ABC$,$D \in \overline{AB}$,$E \in \overline{AC}$ and $\overline{DE} \parallel \overline{BC}$. $F$ is a point on $\overline{AD}$ such that $\overline{EF} \parallel \overline{CD}$. Prove that $AD^2 = AB \times AF$.