$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow DEF$. If $m \angle X = 50^{\circ}$ and $m \angle Y = 75^{\circ}$,then $m \angle F = \dots$ (in $^{\circ}$)

In the figure,$\Delta ODC \sim \Delta OBA$,$\angle BOC = 125^{\circ}$ and $\angle CDO = 70^{\circ}$. Find $\angle DOC$,$\angle DCO$,and $\angle OAB$.

In the given figure,if $\angle D = \angle C$,then is it true that $\triangle ADE \sim \triangle ACB$? Why?

If in two triangles $DEF$ and $PQR$,$\angle D = \angle Q$ and $\angle R = \angle E$,then which of the following is not true?

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AB = 8$ and $BC = 6$,then $BM = \dots$

$CD$ and $GH$ are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that $D$ and $H$ lie on sides $AB$ and $FE$ of $\Delta ABC$ and $\Delta EFG$ respectively. If $\Delta ABC \sim \Delta FEG,$ show that:
$(i) \frac{CD}{GH} = \frac{AC}{FG}$
$(ii) \Delta DCB \sim \Delta HGE$
$(iii) \Delta DCA \sim \Delta HGF$