Question

State which pairs of triangles in Fig. 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 :

Answer 1

( i )

In $△ABC$ and $△PQR$

$\angle A=\angle P$,

$\angle B=\angle Q$,

$\angle C=\angle R$,

$\therefore$ By AAA criterion of similarity, $△ABC\sim △PQR$

( ii )

In $△ABC$ and $△QRP$

$\frac{AB}{QR}=\frac{BC}{RP}=\frac{AC}{QP}=\frac{1}{2}$

$\therefore$ By SSS criterion of similarity, $△ABC\sim △QRP$

( iii )

In $△LMP$ and $△DEF$

$\frac{LM}{DE}=\frac{2.7}{4},\frac{LP}{DF}=\frac{1}{2}$

The sides are not in the equal ratios, Hence the two triangles are not similar.

( iv )

In $△MNL$ and $△QPR$

$\angle M=\angle Q$,

$\frac{MN}{QP}=\frac{ML}{QR}=\frac{1}{2}$

$\therefore$ By SAS criterion of similarity, $△MNL\sim △QPR$

( v )

In $△ABC$ and $△EFD$

$\angle A=\angle F$,

$\frac{AB}{FD}=\frac{BC}{FD}=\frac{1}{2}$

$\therefore$ By SAS criterion of similarity, $△ABC\sim △EFD$

( vi )

In $△DEF$ and $△PQR$

Since, sum of angles of a triangle is ${180}^o$ , Hence, $\angle F={30}^o$ and $\angle P={70}^o$

$\angle D=\angle P$,

$\angle E=\angle Q$,

$\angle F=\angle R$,

$\therefore$ By AAA criterion of similarity, $△DEF\sim △PQR$