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Let ABC and DBC are two isosceles triangles on the same base BC (see figure). Then what is the relation between $∠ A B D and ∠ A C D$ ?

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∠ A B D = ∠ A C D

∠ A B D < ∠ A C D

∠ A B D > ∠ A C D

∠ A B D ≤ ∠ A C D

answer is A.

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Detailed Solution

Given that ABC and DBC are two isosceles triangles on the same base BC.
Question Image

      In △ABC and △DBC,
AB = AC     (From figure)
BD = CD     (From figure)
We know that the angles opposite to equal sides are equal.

Adding both equations (i) and (ii), we get,

Hence, we have

So, option (1) is correct.

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