Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true:
(i)PQ2 + QR2 = RP2
(ii)PQ2 + RP2 = QR2
(iii)RP2 + QR2 = PQ2
From the figure we see that the two angles of a triangle are given and we must find out the third angle by using the angle sum property that is the sum of three interior angles of a triangle is 180°.
We know that, sum of interior angles of a triangle is 180°.
∠P + ∠Q + ∠R = 180°
∠P + 25° + 65° = 180°
∠P + 90° = 180°
∠P = 180° - 90°
∠P = 90°
Thus, triangle PQR is a right angled at P
As one of the angles is 90° that means it is a right-angled triangle and the square of the hypotenuse is equal to the sum of the square of the other two sides.
Therefore, by Pythagoras theorem,
(Perpendicular)2 + (Base)2 = (Hypotenuse )2
Here, Perpendicular = QP, Base = PR and Hypotenuse = QR
(QP)2 + (PR)2 = (QR)2
Hence, option (ii) is correct.
Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true: (i)PQ² + QR² = RP² (ii)PQ² + RP² = QR² (iii)RP² + QR² = PQ²
NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5 Question 6
Angles Q and R of a ∆PQR are 25º and 65º. Option (ii) PQ2 + RP2 = QR2 is the correct result.
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