Question

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC. Which of the following statement is true?

(i) $△$ ADE ~ $△$ ABC

(ii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{D}^2}{A{B}^2}$

(iii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{B}^2}{A{C}^2}$

• A. only (i)
• B. only (i) and (ii)
• C. only (iii)
• D. all (i) , (ii) and (iii)

Answer 1

The correct option is B

only (i) and (ii)

In $△$ ADE and $△$ ABC, we have

$\angle$ ADE = $\angle$ B

[Since DE || BC $\angle$ ADE = $\angle$ B (Corresponding angles)]

and , $\angle$ A = $\angle$ A [Common]

$△$ ADE ~ $△$ ABC

Therefore $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{D}^2}{A{B}^2}$