ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.

Given that

ΔABC is an isosceles triangle having AC = BC and AB2 = 2AC

Triangles Exercise 6.5 Answer 5

In ΔACB,

AC = BC

AB2 = 2AC2

AB2 = AC+ AC2

= AC2 + BC[Since, AC = BC]

By the Pythagoras theorem, ΔABC is a right-angle triangle.

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