Question

ABC is a isosceles triangle with ac equal bc ab square equal 2ac square probe that ABC is a right triangle​

Answer 1

Restatement :

In the adjoining figure ABC is an isosceles triangle with sides AC=BC . Also AB² = 2AC² . To Prove that ABC is a right angled triangle.

Formula to be Used :

If ∆ABC is a right angled triangle , then it will satisfy the Pythagorean theorem , i.e.

$\sf \bullet \: \: Base^{2} + perpendicular^{2} = hypotenuse^{2}$

Proof :

Given ,

AC = BC .........(1)

Again ,

$\sf \implies AB^{2} = 2AC^{2} \\\\ \sf \implies AB^{2} = AC^{2}+ AC^{2} \\\\ \sf \implies AB^{2} = AC^{2} + BC^{2} \:\: \{ \because AC= BC \}$

Thus AB is the hypotenuse and AC and BC are the base and perpendicular.

Therefore , ABC satisfies the Pythagorean theorem ,

Hence ∆ABC is a right angled triangle.

$\bf Hence \: \: proved$