In $\Delta XYZ$,$X-S-Y$,$X-T-Z$ and $\overline{ST} \parallel \overline{YZ}$. If $XS = 4$,$XT = 8$,$SY = x-4$ and $TZ = 3x-19$,find the value of $x$.

In $\Delta ABC$,$m \angle A = m \angle B + m \angle C$. If $AB = 7$ and $BC = 25$,the perimeter of $\Delta ABC = ........$

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at point $D$,then

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

The length of a ladder is $6 \,m$ and it leans on a wall to reach the height of $3.6 \,m$. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

In the given figure,if $\angle 1 = \angle 2$ and $\triangle NSQ \cong \triangle MTR,$ then prove that $\triangle PTS \sim \triangle PRQ.$