If the ratio of corresponding sides of two similar triangles is $2:3$, then the ratio of their corresponding altitudes is

In figure, if $DE\parallel BC$ then $x$ equals to

In the figure below, if $PQ\parallel BC$ and $AP:PB=1:2$. Then $\frac{\mathit{a}\mathit{r}\mathit{ }\left(\mathit{△}\mathit{A}\mathit{P}\mathit{Q}\right)}{\mathit{a}\mathit{r}\mathit{ }\left(\mathit{△}\mathit{A}\mathit{B}\mathit{C}\right)}\mathit{=}$

In given figure $A$, $B$ and $C$ are points on $OP, OQ$ and $OR$ respectively such that $AB\parallel PQ$ and $AC\parallel PR$. Show that $BC\parallel QR$.

In given figure, Two triangles $ABC$ and $DBC$ are on the same base $BC$ in which $\angle A=\angle D=90°$ if $CA$ and $BD$ meet each other at $E$, show that $AE\times CE=BE\times DE$

If the areas of two similar triangles are equal, prove that they are congruent.