In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$

$ABC$ is an equilateral triangle of side $2a$. Find each of its altitudes.

In $\Delta ABC$,$m \angle B = 90$ and $D$ is the midpoint of $\overline{AC}$. Then,$BD = \dots$

In $\Delta ABC$,$AB = 6\sqrt{3} \text{ cm}$,$AC = 12 \text{ cm}$,and $BC = 6 \text{ cm}$. The angle $B$ is (in $^o$):

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 $\Delta PQR,$ the midpoints of the sides are $X, Y, Z.$ In $\Delta XYZ,$ the midpoints of the sides are $A, B, C.$ If the area of $\Delta PQR$ is $240,$ find the area of $\Delta XYZ$ and $\Delta ABC.$