In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AM}$ is an altitude. If $AM = 15$ and the perimeter of $\Delta ABC$ is $50$,find the area of $\Delta ABC$.

In $\Delta XYZ$,$m\angle X = 90^{\circ}$,$XY = 8$ and $YZ = 17$. Then,the area of $\Delta XYZ$ is.............

In $\Delta ABC$,$m\angle B = 90^{\circ}$,$AB = 2x + 3$,$BC = x + 2$,and $AC = 3x - 1$. Find the value of $x$.

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 $\Delta ABC.$

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 6$,$XZ = 8$ and $YM = 4.2$,find $YZ$.

For the correspondence $ABC \leftrightarrow XYZ$ being a similarity, which of the following correctly matches the information in Part $I$ and Part $II$?

Part $I$	Part $II$
$1.$ In $\Delta ABC$ and $\Delta XYZ, \frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$	$a. SSS$ condition
$2.$ In $\Delta ABC$ and $\Delta XYZ, \angle A \cong \angle X, \angle B \cong \angle Y$ and $\angle C \cong \angle Z$	$b. SAS$ condition
$3.$ In $\Delta ABC$ and $\Delta XYZ, \frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX}$	$c. AAA$ condition
-	$d. \text{None of the conditions apply}$