In the given figure, if AB = AC and D is the midpoint of BC, then which of the

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In the given figure, if AB = AC and D is the midpoint of BC, then which of the following is true ?

Options:

A .

△ A D B ≅ △ A D C

by RHS postulate

B .

△ A D B ≅ △ A D C

by SSS postulate

C . AB bisects

∠ B A C

D . If

∠ B A C = 80^{\circ},

then

∠ A B D = 80^{\circ}

Answer: Option B
:
B

In $△ A B D$ and $△ A C D$

(i) AB = AC .........(given)

(ii) BD = CD .........(given)

(iii) AD = AD ..........(common)

(iv) $△ A B D ≅ △ A C D$ ......(SSS Postulate)

(v) $∠ B A D = ∠ C A D$ .....(cpct)

$∴$ AD bisects $∠$ BAC

(vi) $∠ A B D = ∠ A C D$ .....(cpct)

If $∠ B A C = 80^{\circ}$ , then $∠ A B D = ∠ A C D = 50^{\circ}$ ( not $80^{\circ}$ )

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