Question

Prove that the sum of the interior angles of a triangle is


180°​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: proof:}}}}$

Let,

• There be any triangle with vertices ABC.

To prove :

• Sum of all angles add upto 180°. That is, ∠A+∠B+∠C = 180.

Refer to the attachment: I have marked these angles as ∠1, ∠2 and ∠3 in correspondence with A,B and C.

Construction :

• Through A, draw a line m parallel to BC.

Proof :

Since m || BC.

Therefore,

1. ∠2 =∠4 (By alternate angles)
2. ∠3 =∠5 (By alternate angles)

Adding eq (i) and eq (ii)

⇒ ∠2 +∠3 =∠4 +∠5

Adding ∠1 both side:

⇒∠1 +∠2 +∠3= ∠1 +∠4 +∠ 5

⇒∠1 + ∠2 +∠3= 180

Because ∠1, ∠4 and ∠5 all the angles lies on the same straight line. Hence their sum would be 180°.

So,

The sum of three angles of a triangle is 180

Hence, proved!!

Answer 2

Answer:

Construction of triangle

Step 1 - First draw a triangle ABC

Step 2 - Then draw a line on the upper

Step 3 - Then mark the vertices.

Proof

Since m||BC

So,

$\angle \: 2 = \angle4 \: (alternate \: angle)$

$\angle3 = \angle \: 5 \: (alternate \: angle)$

Adding equation 1 and 2

$\angle 2 + \angle3 = \angle 4 + \angle 5$

$\angle \: 1 + \: \angle2 \: +\angle3 = \angle1+ \: \angle4 +\: \angle5$

So ∠1, ∠4 and ∠5 all the angles lies on the one and same straight line. Hence their sum would be 180°.

Hence proved