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

Solution:

We know that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In ΔABC, ∠ACB = 90° and AC = BC [Since, ABC is an isosceles triangle right angled at C]

Using Pythagoras theorem,

⇒ AB² = AC² + BC²

⇒ AB² = AC² + AC²  [Since  AC = BC]

Therefore, AB² = 2 AC²

☛ Check: NCERT Solutions for Class 10 Maths Chapter 6

Video Solution:

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

NCERT Class 10 Maths Solutions Chapter 6 Exercise 6.5 Question 4

Summary:

For a triangle ABC that is an isosceles triangle right angled at C, it is proved that AB² = 2AC².

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