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In figure, $ABC$ is an isosceles triangle in which $AB = AC .$ $E$ is a point on the side $CB$ produced such that $FE ⊥ AC$ . If $AD ⊥ CB$ , state if “ $AB × EF = AD × EC$ ” is true or false.

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False

True

answer is B.

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Detailed Solution

It is given that

ABC

is an isosceles triangle in which

FE ⊥ AC

and

AD ⊥ CB

.
In triangle ABD and ECF,

A B = A C ∠ B = ∠ C

Δ A B D & Δ E C F ∠ A B D = ∠ E C F

Δ A B D ~ Δ E C F

(By AA similarity)
Now,

∠ A D B = ∠ E F C A B E C = A D E F A B × E F = A D × E C

Hence

A B × E F = A D × E C

.
Hence, option 2 is correct.

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