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  • ABC is an isosceles triangle with AC = BC. If AB ^2 = 2 AC ^ 2, prove that ABC is a right triangle.

Q5 ABC is an isosceles triangle with AC = BC. If AB ^ 2 = 2 AC ^ 2 , prove that ABC is a right triangle.

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Given: ABC is an isosceles triangle with  AC=BC.

In \triangle ABC,

AB^2=2.AC^2                 (Given )

AB^2=AC^2+AC^2           (AC=BC)

AB^2=AC^2+BC^2

These sides satisfy Pythagoras theorem so ABC is a right-angled triangle.

Hence proved 

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