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 $AC$.

It is given that $\triangle DEF \sim \triangle RPQ.$ Is it true to say that $\angle D = \angle R$ and $\angle F = \angle P?$ Why?

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB^2 + AC^2 = 122$ and $AD = 6$,find $BC$.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overleftrightarrow{PQ} \parallel \overleftrightarrow{BC}$. If $AP = 3$,$PB = 5$ and $AQ = 6$,find $QC$ and $AC$.

$\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow DEF$. If $3 AB = 5 DE$ and $DF = 9$,then $AC = \ldots$

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $CM = 3$,then $BM = \dots$