Question 5 ABC is an isosceles triangle with AC = BC. If AB2=2AC2, prove that ABC is a right triangle.
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Solution
Given that ΔABC is an isosceles triangle having AC = BC and AB2=2AC2 In ΔABC, AC = BC (Given) ⇒AB2=2AC2 (Given) ⇒AB2=AC2+AC2 ⇒AB2=AC2+BC2 [Since, AC = BC] Hence, by using Pythagoras theorem ΔABC is right angled triangle.