Table of Contents
- Angle Sum Property of a Triangle – Proof
- What’s Next?
In the previous segment, we took a logical approach to understand how the sum of the angles of a triangle is 180 degrees. In this segment, we will look at a systematic approach to prove the same.
Angle Sum Property of a Triangle – Proof
To prove: The sum of all angles within a triangle is 180°.
That is, in △ABC, ∠A + ∠B + ∠C = 180°.
Triangle ABC
Construction: Draw a line EF passing through point A and parallel to BC.
Let the interior angles of triangle ABC be 1, 2, and 3 and the angles formed outside the triangle be 4 and 5 as shown.
Construction for Proof
| 1 | Sides AB and AC are actually transversals cutting through the parallel lines BC and EF. | From construction |
| 2 | ∠2 ≅ ∠4 | ∠2 and ∠4 are the alternate interior angles formed by transversal AB |
