Q. 15 A35.0( 3 Votes )

# In an isosceles triangle ABC, if AC = BC and AB^{2} = 2AC^{2}, then the measure of C is

A. 30°

B. 90°

C. 45°

D. 60°

Answer :

Given: AB^{2} = 2AC^{2}

⇒ AB^{2} = AC^{2} + AC^{2}

⇒ AB^{2} = AC^{2} + BC^{2} [∵ Given: AC = BC]

The expression given above is equivalent to expression of Pythagoras theorem, h^{2} = p^{2} + b^{2}, which corresponds to a right angled triangle.

Also, h = AB and angle opposite to hypotenuse is right angle.

Thus ∠C = 90°.

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