Q15 of 27 Page 289

In an isosceles triangle ABC, if AC = BC and AB2 = 2AC2, then the measure of C is

Given: AB2 = 2AC2


⇒ AB2 = AC2 + AC2


⇒ AB2 = AC2 + BC2 [∵ Given: AC = BC]


The expression given above is equivalent to expression of Pythagoras theorem, h2 = p2 + b2, 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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