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

1.	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» ∵ 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.

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»

∵ 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.