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in Triangles by (38.0k points)
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ABC, is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =

A. 55°

B. 70°

C. 35°

D. 110°

1 Answer

+1 vote
by (36.4k points)
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Best answer

For an isosceles triangle

∠ABC = ∠ACB = 35°

Let the ∠ADB be x

Then,

∠ADC = 180° - x

As AD is median so BD = CD

And for isosceles triangle AB = AC

So,

\(\frac{AB}{AC}\) = \(\frac{BD}{CD}\) = 1

By angle bisector theorem,

∠BAD = ∠CAD = y (Let)

For ΔBAD

35 + x + y =180 (i)

For ΔDAC

35 + 180 – x + y = 180 (ii)

35 + y = x

Therefore,

35 + 34 + y + y = 180°

2y + 70 = 180°

2y = 100°

y = 55°

Therefore,

∠BAD = ∠CAD = 55°

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