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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}

**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,

⇒ AB^{2} = AC^{2} + BC^{2}

⇒ AB^{2} = AC^{2 }+ AC^{2 } [Since AC = BC]

Therefore, AB^{2} = 2 AC^{2}

**☛ 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 AB^{2} = 2AC^{2}.

**☛ Related Questions:**

- ABC is an isosceles triangle with AC = BC. If AB^2 = 2AC^2, prove that ABC is a right triangle.
- ABC is an equilateral triangle of side 2a. Find each of its altitudes.
- Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.
- In Figure 6.54, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that(i) OA2 + OB2 + OC2 - OD2 - OE2 - OF2 = AF2 + BD2 + CE2(ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2

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