Criteria for Similarity of Triangles

SSS similarity criterion: If in two triangles, corresponding sides are in the _____, then their corresponding angles are equal and hence the triangles are _____.

$\mathrm{SAS}$ similarity criterion: If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the$.........$, then the triangles are similar.

$AAA$ similarity criterion: If in two triangles, corresponding angles are equal, then their$.........$are in the same ratio and hence, the two triangles are similar.

If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are _____ to the whole triangle and also similar to each other.

AA similarity criterion: If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are _____.  $\left(\mathrm{Similar} / \mathrm{Congruent}\right)$

The area of two similar triangles $\mathrm{ABC}$ and $\mathrm{PQR}$ are $25 {\mathrm{cm}}^2$ and $49 {\mathrm{cm}}^2$. If $\mathrm{QR}=9.8 \mathrm{cm}$, then $\mathrm{BC}$ is:

If $∆ABC~∆RQP$, $\angle A={80}^o$ and $\angle B={60}^o$, then the value of $\mathrm{\angle }P$ is

If $∆PQR~∆XYZ$, $\angle Q=50°$ and $\angle R=70°$, then $\angle X$ is equal to