Question

Which of the following is correct about the following triangles?

• A. ∆ABC $\sim$ ∆MNR
• B. ∆ABC $\sim$ ∆RMN
• C. ∆ABC $\sim$ ∆MRN
• D. ∆ABC $\sim$ ∆RNM

Answer 1

The correct option is A ∆ABC $\sim$ ∆MNR

$\text{Given:}\angle A=80°,\angle C=70°\angle M=80°,\angle N=30°$

$\text{In ΔABC,}\angle B=180°–(80°+70°)=30°$
$\text{(Sum of interior angles of a triangle}\text{is 180°.)}$

$\text{Now, consider ΔABC and ΔMNR,}\angle A=\angle M=80°\angle B=\angle N=30°$

$\therefore \Delta ABC\sim \Delta MNR\text{(By AA similarity criterion)}$