Math, asked by tikendrajitoinam, 6 months ago

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

Answered by Cynefin
67

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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)

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Answered by Itzdazzledsweetìe02
60

✏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

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