Question

Choose the correct option.

• A. $\Delta DEF\sim \Delta PRQ$
• B. $\Delta FED\sim \Delta RQP$
• C. $\Delta DEF\sim \Delta PQR$
• D. $\Delta DEF\sim \Delta RQP$

Answer 1

The correct option is D $\Delta DEF\sim \Delta RQP$

$\text{Given: DE = 2.5 cm, DF = 3 cm}\text{and EF = 2 cm}$

$\text{PQ = 4 cm, PR = 6 cm and}\text{QR = 5 cm}$

$\text{In ΔDEF and ΔPQR,}$

$\frac{DE}{QR}=\frac{2.5}{5}=\frac{1}{2}$

$\frac{DF}{PR}=\frac{3}{6}=\frac{1}{2}$

$\frac{EF}{PQ}=\frac{2}{4}=\frac{1}{2}$

$\therefore \Delta DEF\sim \Delta RQP\text{(By SSS similarity criterion)}$