Question

In the given figure, 0 is a point inside a ∠PQR such that ∠POR = 90°, OP = 6 cm and OR= 8 cm. If PQ = 24 cm and QR = 26 cm, prove that ΔPQR is right angled P.

Answer 1

Given: ∠POR = 90°, OP = 6 cm and OR= 8 cm and PQ = 24 cm and QR = 26 cm

To Prove: ∆PQR is right angled at P

In ∆POR, using Pythagoras theorem, we get

(Perpendicular)² + (Base)² = (Hypotenuse)²

⇒ (PO)² + (OR)² = (PR)²

⇒ (6)² + (8)² = (PR)²

⇒ 36 +64 = (PR)²

⇒ (PR)²= 100

⇒ PR =√100

⇒ PR = 10 [taking positive square root]

In ∆PQR

Using Pythagoras theorem, i.e. if the square of the hypotenuse is equal to the sum of the other two sides. Then, the given triangle is a right angled triangle, otherwise not.

Here, (PR)² + (PQ)²

⇒ (10)² + (24)²

= 100 + 576

= 676

= (26)² = (QR)²

∴ Given sides 10cm, 24cm and 26cm make a right triangle right angled at P.

Hence Proved