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ABC is an isosceles triangle with AC = BC. If \(AB^2 = 2AC^2\), prove that ABC is a right triangle.
Answer :
Given, \(\triangle\)ABC is an isosceles triangle having AC = BC and \(AB^2 = 2AC^2\)
In \(\triangle\) ACB,
AC = BC
\(AB^2 = 2AC^2\)
\(AB^2 = AC^2 + AC^2\)
= \(AC^2 + BC^2\) [Since, AC = BC]
Hence, by Pythagoras theorem \(\triangle\) ABC is right angle triangle.