Question

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

Answer 1

▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬

$\huge\boxed{ANSWER}$

▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬

Refer to attachment.

Answer 2

$\bf\huge\mathfrak{Answer}$

Given -

ABC is an isosceles triangle with AC = BC. AB² = 2AC²

To Prove -

ABC is a right angled triangle.

That is, ∠C = 90°

Proof -

AB² = 2AC² - (Given)

AB² = AC² + AC²

AB² = AC² + BC² - (As AC = BC)

Thus, AB is the largest side ie the Hypotenuse.

By the Converse of Pythagoras theorem,

∠C = 90°

Hence its a right angle triangle.

$\bf\huge\mathfrak{Hence\:proved}$