The sum of the angles of a triangle is 180° Theorem 6.7 Class 9
Theorem 6.7 : The sum of the angles of a triangle is 180°.
Given: PQR with ∠1, ∠2 and ∠3
Prove: ∠1 + ∠2 + ∠3= 180°
Construction: Through A draw a line XY parallel to BC.
Proof:
⇒For lines PQ & BC
⇒AB is the transversal.
∠4 = ∠2 (Alternate Interior Angle)
⇒For lines PQ & BC
⇒AC is the transversal.
⇒∠5 = ∠3 (Alternate Interior Angle)
⇒As PAQ is a straight line
⇒∠1 + ∠4 + ∠5 = 180°
⇒∠4 = ∠2 and ∠5 = ∠3 (Above Proved)
⇒So, ∠1 + ∠2 + ∠3 = 180°
⇒Hence, the sum of all angles of a triangle is equal.
⇒Hence proved
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