Question

For the given triangles, which of the following is true?

• A. $△ABC\sim △PQR$
• B. $\Delta ABC\sim \Delta QPR$
• C. $\angle BCA=\angle PRQ$
• D. $\angle BAC=\angle QPR$

Answer 1

Answer: (B), (C)

The correct options are
B $\Delta ABC\sim \Delta QPR$
C $\angle BCA=\angle PRQ$

$\text{Given:}\angle A=\angle Q...\left(i\right)\angle B=\angle P...\left(ii\right)$

$\text{We know that, the sum of the angles}\text{in a triangle is}{180}^{\circ }.$
$⟹\angle C={180}^{\circ }-\angle A-\angle B...\left(iii\right)$
$⟹\angle R={180}^{\circ }-\angle P-\angle Q...\left(iv\right)$

$\text{From (i), (ii) and (iv), we get:}\angle R={180}^{\circ }-\angle A-\angle B...\left(v\right)$

$\text{From (iii) and (v), we get:}⟹\angle C=\angle R⟹\angle BCA=\angle PRQ$

$\text{Corresponding angles are equal in}\text{similar triangles.}\text{Hence,}\Delta ABC\sim \Delta QPR$