Question

ABC is an isosceles triangle , right angled at C . prove that AB²=2AC²

Answer 1

because it is given that it is perpendicular at c

so ab is hypotenuse
and ac and bc are other two sides

we know that by pythagoras theorem

${ab}^{2} = {ac}^{2} + {bc}^{2}$
as the triangle is isosceles triangle

so bc=ac
${ab}^{2} = {ac}^{2} + {ac}^{2} \\ \\ {ab}^{2} = 2 {ac}^{2}$

Answer 2

GIVEN : a triangle ABC where AC = BC

             ∠C = 90°

TO PROVE :  AB² = 2AC²

PROOF : IN ΔABC,  by hypotenuse theorem

                             AB² =  AC² + BC²

given AC = BC

                       ∴  AB² = AC² + AC²

                       ⇒ AB² = 2AC²