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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) area of  ADEarea of  ABC = AD2AB2

(iii) area of  ADEarea of  ABC = AB2AC2



A

only (i)

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B

only (i) and (ii)

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C

only (iii)

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D

all (i) , (ii) and (iii)

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Solution

The correct option is B

only (i) and (ii)


In ADE and ABC, we have

ADE = B

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

and , A =  A  [Common]

ADE ~ ABC

Therefore area of  ADEarea of  ABC = AD2AB2


Mathematics

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