Q. 5 4.2( 94 Votes )

ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2prove that ABC is a right triangle.

Answer :

To Prove: ABC is a right angled triangle
Given: AB2 = 2AC2

Now 2 AC2 can be split into two parts

AB2 = AC2 + AC2

in an isosceles triangle ABC two sides are equal, and it is given that AC = BC. So,

AB2 = AC2 + BC2 (As, AC = BC)   

Now According to pythagoras theorem, in a right angled triangle, square of one side equals to the sum of squares of other two sides
And clearly above equation satisfies it. Thus, the equation satisfies pythagoras theorem and the triangle should be right angled for that.

Therefore, the given triangle is a right-angled triangle
Hence, Proved.

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