In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 2.5$,$MB = 3$ and $AN = 3.75$,find $AC$.

Using Theorem $6.2$,prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

In rhombus $ABCD$,$AC = 24$ and $BD = 70$. Find the perimeter of rhombus $ABCD$.

$A$ line drawn parallel to $\overline{YZ}$ in the plane of $\Delta XYZ$ passes through the midpoint of $\overline{XY}$. Prove that this line bisects $\overline{XZ}$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $BM = 12$ and $CM = 18$,find $AB$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AB = 20$ and $AC = 29$,find the perimeter of $\Delta ABC$.