Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:
Option 1: Isosceles triangle
Option 2: Right-angled triangle
Option 3: Equilateral triangle
Option 4: Right isosceles triangle
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Correct Answer: Right isosceles triangle
Solution : AB = $k$ BC = $k$ AC = $\sqrt2k$ ⇒ AB 2 = $k^2$ ⇒ BC 2 = $k^2$ ⇒ AC 2 = $2k^2$ $\therefore$ AB 2 + BC 2 = AC 2 and AB = BC By Pythagoras theorem, $\triangle$ ABC is a right isosceles triangle. Hence, the correct answer is 'Right isosceles triangle'.
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