Theorem 6.7 : Angle sum property of triangle Class 9

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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Angles opposite to equal sides of an isosceles triangle are equal Theorem 7.2 Class 9

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