Q.6 Angles Q and R of a APQR are 25° and 65°. Write which of the following is true.

(i) \( PQ^2 + QR^2 = RP^2 \)

(ii)\( PQ^2 + RP^2 = QR^2 \)

(iii)\( RP^2 + QR^2 = PQ^2 \)

(i) \( PQ^2 + QR^2 = RP^2 \)

(ii)\( PQ^2 + RP^2 = QR^2 \)

(iii)\( RP^2 + QR^2 = PQ^2 \)

We know that

\(\angle P + \angle Q + \angle R = 180° \)(Angle sum property)

\(\angle \)P + 25° + 65° = 180°

\(\angle \)P + 90° = 180°

\(\angle \)P = 180° – 90° – 90°

\(\triangle \)PQR is a right triangle, right angled at P

(i) Not True

\(\therefore PQ^2 + QR^2 \neq RP^2 \) (By Pythagoras property)

(ii) True

\(\therefore \) \(PQ^2 + RP^2 = QP^2 \) (By Pythagoras property)

(iii) Not True

\(\therefore RP^2 + QR^2 \neq PQ^2 \)(By Pythagoras property)