In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 12$,$AC = 20$,and $MB = 9$,find $MD$.

If in two right triangles,one of the acute angles of one triangle is equal to an acute angle of the other triangle,can you say that the two triangles will be similar? Why?

In triangles $ABC$ and $DEF$,$\angle B = \angle E$,$\angle F = \angle C$ and $AB = 3 DE$. Then,the two triangles are

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$.
If $m \angle X : m \angle Y : m \angle Z = 2 : 3 : 5$,then in $\Delta DEF$,$\ldots \ldots$ is a right angle.

In the figure,altitudes $AD$ and $CE$ of $\Delta ABC$ intersect each other at the point $P$. Show that $\Delta PDC \sim \Delta BEC$.

$\Delta ABC$ and $\Delta XYZ$ are similar under the correspondence $ABC \leftrightarrow XZY$. If $AB = 6$,$XY = 12$,$YZ = 6$,and $ZX = 9$,find the perimeter of $\Delta ABC$.