Class 9 Maths Lines and Angles Angle Sum Property of Triangle

Angle Sum Property of Triangle

Theorem 7: The sum of the angles of a triangle is 180o.

Since this is a theorem, let’s try to prove it.

To prove: ∠ 1 + ∠ 2 + ∠ 3 = 180o

Proof: 

∠4 = ∠ 3               (Alternate angle theorem) – (i)

∠5 = ∠ 2               (Alternate angle theorem) – (ii)

Now,

∠ 1 + ∠ 4 + ∠ 5 = 180o, Since EF is a line.

Or,  ∠  1 + ∠ 3+ ∠2 = 180o ,Replacing ∠4 with ∠ 3 & ∠5 with ∠ 2 as per eq i & ii.

 

 

Exterior Angle of a triangle: Side QR of triangle PQR is produced to point S, ∠ ACD is called an exterior angle of ΔABC

Theorem 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

Since this is a theorem, let’s try to prove it.

To prove: ∠9 = ∠ 6 + ∠ 8 

Proof: 

∠7 + ∠ 6 + ∠ 8 = 180o  (Angle Sum property of Triangle) – (i)

∠7 + ∠ 9 = 180o                (Linear Pair as BCD is a line) – (ii)

 

Comparing i & ii , we can say that, ∠9 = ∠ 6 + ∠ 8 

 

 

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