Question

Find the criteria to prove $\Delta ABC\sim \Delta PQR$ for the following conditions.

• A. AA similarity
• B. SSS similarity
• C. SAS similarity

Answer 1

Consider the $\Delta ABC$ and $\Delta PQR$

1. Given $\angle A=\angle P$ and $\angle C=\angle R$
$\to$Two pair of corresponding angles are equal.

$\therefore$ $\Delta ABC\sim \Delta PQR$ by AA similarity.

2. Given $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$
$\to$All three pair of corresponding sides are proportional.

$\therefore$ $\Delta ABC\sim \Delta PQR$ by SSS similarity.

3. Given $\frac{AC}{PR}=\frac{BC}{QR}$ & $\angle R=\angle C$
$\to$Two pair of corresponding sides are proportional and corresponding included angles are equal.

$\therefore$ $\Delta ABC\sim \Delta PQR$ by SAS similarity.