Question

Study the following figures and find out in each case whether the triangles are similar. Give reason.

Answer 1

$i)$ In $△DGH$ & $△DFE$

$\angle D=\angle D$ (Common)

$\angle DHG=\angle DEF$ (Corresponding angle)

$\angle DGH=\angle DFE$ (Corresponding angle)

$\therefore △DGH\sim △DFE$ (by $AAA$)

$ii)$ If angles are a° then $△ABC$ &$△DEF$ are similar to each other.

$iii)$ $△POQ$ & $△MON$

$\frac{OP}{OM}=\frac{6}{6+2}=\frac{6}{8}=\frac{3}{4}$

$\frac{OQ}{ON}=\frac{8}{8+2}=\frac{8}{10}=\frac{4}{5}$

$\frac{PQ}{MN}=\frac{4}{6}=\frac{2}{3}$

$\therefore$ All ratio are not equal. So, triangles are not similar.

$iv)$ In $△XUV$ & $△XYZ$

$\frac{XU}{XY}=\frac{a}{2a+a}=\frac{a}{3a}=\frac{1}{3}$

$\frac{XV}{XZ}=\frac{c}{2c+c}=\frac{c}{3c}=\frac{1}{3}$

$\frac{UV}{YZ}=\frac{b}{3b}=\frac{1}{3}$

$\therefore$ All ratio's are equal. So, given $△XUV$ & $△XYZ$ are similar to each

other.