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In $△ A B C$ , is isosceles with AB=AC, $A B ⊥ A C;$ Which of the following is a correct statement?

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$△ A B D ≅ △ A C D$

$△ A D B ≅ △ A C D$

$△ A D C ≅ △ A B D$

$△ A B C ≅ △ A D C$

answer is B.

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Detailed Solution

In the figure , given below:

Checking congruence of the triangle $△ A B D ≅ △ A C D$ , we get

Right angle, $∠ B D A = ∠ C D A = 90^{o}$ ,

Hypotenuse, AB=AC

Side BD=CD

Hence. triangles are congruent by RHS property.

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