In /\ PQR ;PQ =√8,QR= √5,PR=√3.In /\ PQR is a right angled triangle?If yes which is 90°?
Answers
Answer:
∠R = 90°
Step-by-step explanation:
Given:
ΔPQR
PQ = √8
QR = √5
PR = √3
To prove:
ΔPQR is a right-angled triangle and to find which angle is 90°.
Proof:
PQ =√8
Squaring on both sides
⇒PQ² = (√8)²
∴PQ² = 8 ______(1)
QR= √5
Squaring on both sides
⇒QR² = (√5)²
∴QR² = 5 ______(2)
PR=√3
Squaring on both sides
⇒PR² = (√3)²
∴PR² = 3 _______(3)
from (1), (2) and (3)
⇒8 = 5 + 3
⇒PQ² = QR² + PR²
∴PQ² = QR² + PR²
This ΔPQR satisfied the Pythagoras theorem.
By Pythagoras theorem
If a triangle is right-angled then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
⇒Hypotenuse² = side₁² + side₂²
∴ΔPQR is a right=angled triangle.
Hypotenuse = PQ
The angle which is opposite to hypotenuse is 90°.
⇒The angle opposite to PQ is ∠R
∴∠R = 90°
Step-by-step explanation:
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