Theorem 6 8 class 9th

Mathematics Theorem
For Class 9TH
THEOREM 6.8:
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two
interior opposite angles.
Ρ
1
Given: A Δ PQR, QR is produced to point S.
Where ∠PRS is exterior angle of Δ PQR.
4
To Prove: ∠4 = ∠1 + ∠2
2
3
Q
R
Proof:
Statements
Reasons
For line QS
∠3 + ∠4 = 180
(Linear pair) ……. (1)
In Δ PQR
∠1 + ∠2 + ∠3 = 180
(Angle sum property of triangle) …..(2)
From (1) and (2)
∠3 + ∠4 = ∠1 + ∠2 + ∠3
∠4 = ∠1 + ∠2
∠PRS = ∠RPQ + ∠PQR
Hence, exterior angle is sum of two opposite interior angles.
Hence proved.
S
Name:
Description:
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