Question

Which of the following is correct for the following triangles?

• A. ∆ABC $\sim$ ∆PQR
• B. ∆ACB $\sim$ ∆RQP
• C. ∆ABC $\sim$ ∆RQP
• D. ∆ACB $\sim$ ∆PQR

Answer 1

The correct option is B ∆ACB $\sim$ ∆RQP

Given: AC = 8 cm and BC = 6 cm
PQ = 4.5 cm, QR = 6 cm

In ∆ABC and ∆PQR,

∠C = ∠Q = 80° (given)

$\frac{AC}{BC}=\frac{8}{6}=\frac{4}{3}$

and $\frac{QR}{PQ}=\frac{6}{4.5}=\frac{4}{3}$

$\Rightarrow$ $\frac{AC}{BC}=\frac{QR}{PQ}$

$\therefore$ ∆ACB $\sim$ ∆RQP (by SAS similarity criterion)