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In $Δ A B C,$ if $A D A E = B D E C$ and $∠ A D E = ∠ A C B$ then $Δ A B C$ is

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right-angled triangle

isosceles triangle

equilateral triangle

scalene triangle

answer is B.

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Detailed Solution

It is given that

A D A E = B D E C

and

∠ A D E = ∠ A C B

.
Let us draw the figure.
Question Image

So, by using basic proportionality theorem, we get DE∥BC.
So, ∠ADE = ∠DBC (corresponding angles) and
∠ADE = ∠ECB
So, DBC

= ∠

ECB
So opposite angles are equal.
Hence, opposite sides are also equal.
It is an isosceles triangle.
Hence, the correct option is 2.

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