Question

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

Answer 1

Data: ABC is an isosceles triangle with AC = BC.

AB² = 2AC² . 

To Prove: ∆ABC is a right angled triangle 

AB² = 2AC² (Data) 

AB² = AC² + AC² 

AB² = AC² + BC² (∵ AC = BC) 

Now, in ∆ABC, square of one side is equal to squares of other two sides. 

∆ABC is a right angled triangle, Opposite angle to AB, i.e., ∠C is 90°.