Q. Angles Q and R of a Triangle PQR are 25 degrees and 65 degrees. Write which of the following is true: (1). PQ² + QR² = RP² (2). PQ² + RP² = QR² (3). RP² + QR² = PQ².
Answers
GiveN:
- Here is a triangle whose two angles are given.
- Angle Q and Angle R are 25° and 65°
To FinD:
Which of the following statement will be true?
- PQ² + QR² = RP²
- PQ² + RP² = QR²
- RP² + QR² = PQ².
Step-wise-Step Explanation:
By using Angle sum property of triangles, the measure of angle P is:
⇒ Angle P + Angle Q + Angle R = 180°
⇒ Angle P + 25° + 65° = 180°
⇒ Angle P + 90° = 180°
⇒ Angle P = 90°
So, ∆PQR is a right angled triangle. The largest angle is Angle P i.e. 90°. That means, QR is the longest side of ∆PQR because side opposite to largest angle is the largest. PQ and PR are the Perpendicular and base of the triangle.
According to Pythagoras theoram,
⇒ (Perp.)² + (Base)² = (Hypotenuse)²
⇒ PQ² + PR² = QR²
Hence, the Correct Option is PQ² + RP² = QR² (2)
✏QUESTION
Angles Q and R of a triangle PQR are 25° and 65°. Write which of the following is true:
- (i) PQ²+ QR²= RP²
- (ii) PQ²+ RP²= QR²
- (iii) RP² + QR²= PQ²
✏SOLUTION
In ∆ PQR,
∠Q = 25°, ∠R = 65°, ∠P = ?
By Angle Sum Property,
∠P + ∠Q + ∠R = 180°
∠P + 25° + 65° 180°
∠P + 95° = 180°
∠P = 180°-90°
∠P = 90°
PQR is a right angled triangle.
By Pythagoras Theorem,
QR² = PQ²+ RP²=
i.e. PQ² = RP²+ QR²
Hence (ii) is true
__________________________
✏KNOWLEDGE REQUIRED
☯Phytagoras Theorem.
In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides This is known as Pythagoras Theorem.
☯Formula
a ²+ b²= c²
a= side of right triangle
b= side of right triangle
c = hypotenuse