Prove that the sum of the three angles of a triangle is 180°
Solution:
Consider a triangle ABC.
Draw a line l through A, parallel to BC.
We have to prove that ∠A + ∠B + ∠C is equal to 180 degrees.
The measure of A = ∠1
B = ∠2
C = ∠3
Given, l || BC
We know that the alternate angles are equal in parallel lines.
∠2 = ∠4 -------------- (1)
∠3 = ∠5 -------------- (2)
Adding (1) and (2),
∠2 + ∠3 = ∠4 + ∠5
By adding ∠1 on both sides,
∠1 + ∠2 + ∠3 = ∠4 + ∠5 + ∠1
From the figure,
The sum of the angles at a point on a line is equal to 180 degrees.
∠4 + ∠1 + ∠5 = 180°
So, ∠1 + ∠2 + ∠3 = 180°
Therefore, ∠A + ∠B + ∠C = 180°
✦ Try This: Iron roads a, b, c, d, e and f are making a design in a bridge as shown in Fig., in which a ∥b, c∥d, e∥ f. Find the marked angles between d and e.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.4 Sample Problem 2
Prove that the sum of the three angles of a triangle is 180°
Summary:
Two angles, formed when a line crosses two other lines, lie on opposite sides of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees
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