Neha Tyagi and Amit Rastogi Solutions for Chapter: Triangles, Exercise 2: Exercise

In $△\mathrm{PQR}$ and $△\mathrm{MST},\angle \mathrm{P}=55°,\angle \mathrm{Q}=25°,\angle \mathrm{M}=100°$ and $\angle \mathrm{S}=25°$. Is $△\mathrm{QPR}~△\mathrm{TSM}$? 

Two quadrilaterals are similar, if their corresponding angles are equal.

If the two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle, then the two triangles are similar.

If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then the two triangles will be similar.

The ratio of the corresponding altitudes of two similar triangles is $\frac{3}{5}$. The ratio of their areas is $\frac{6}{5}$.

$D$ is a point on side $QR$ of $△\mathrm{PQR}$ such that $\mathrm{PD}\perp \mathrm{QR}$. Will it be correct to say that $△\mathrm{PQD}~△\mathrm{RPD}$ ? Why ?

In the figure, if $\angle D=\angle C$, then $△ADE~△ACB$.

If in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar.