Question

Are the triangles in the given figure similar? If yes, by which test ?

Answer 1

Given:
PQ = 6
PR = 10
QR = 8
LM = 3
LN = 5
MN = 4
Now,
$$\begin{gathered} \frac{\mathrm{PQ}}{\mathrm{LM}}=\frac{6}{3}=2, \\ \frac{{\displaystyle \mathrm{QR}}}{{\displaystyle \mathrm{MN}}}=\frac{{\displaystyle 8}}{{\displaystyle 4}}=2, \\ \frac{{\displaystyle \mathrm{RP}}}{{\displaystyle \mathrm{NL}}}=\frac{{\displaystyle 10}}{{\displaystyle 5}}=2 \end{gathered}$$
$\therefore \frac{\mathrm{PQ}}{\mathrm{LM}}=\frac{{\displaystyle \mathrm{QR}}}{{\displaystyle \mathrm{MN}}}=\frac{{\displaystyle \mathrm{RP}}}{{\displaystyle \mathrm{NL}}}$
By SSS test of similarity
△PQR ∼ △LMN