Sides of two similar triangles are in the ratio $4:9$. Areas of these triangles are in the ratio

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QPR.$ If $m \angle P : m \angle Q : m \angle R = 2 : 3 : 4,$ then $m \angle A : m \angle B : m \angle C = \ldots$

Is the triangle with sides $25 \, cm$,$5 \, cm$,and $24 \, cm$ a right triangle? Give reasons for your answer.

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

State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 10$,$MB = 8$,and $MC = 5$,find $BD$.