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


Answer :

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)

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