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