Question

In ∆PQR ∠Q = 25° and ∠R = 65° which of the following statement is true?

(i) PQ² + QR² = RP²

(ii) PQ² + RP² = QR²

(iii) RP² + QR² = PQ²

Answer 1

∵ The sum of all three angles of a triangle is always 180°.

∴ ∠P + ∠Q +∠R = 180°
⇒ ∠P + 25° + 65° = 180°
⇒ ∠P + 90° = 180°
⇒ ∠P = 180° – 90° = 90°

∴ ∆PQR is a right angled triangle where ∠P = 90°

∴ From Pythagorous Theorem PR² + PQ² = QR²
= QR²

∴ (ii) is true.