Triangle Angle Sum Theorem: A More Friendly Proof

Introduction

In high school mathematics, we were taught to write proofs in two columns. There are some proofs however that are easier to understand if we use Algebra. The triangle angle sum theorem that I have posted yesterday can be proven algebraically. Its proof which I think is easier to understand is shown below.

triangle angle sum

Theorem

The sum of the interior angles of a triangle is 180^{\circ}

Proof

Let ABC be a triangle with angle measures \alpha, \beta, and \gamma. In the figure above, angles having the same Greek letters are congruent since they are alternate interior angles. Now, \alpha + \beta + \gamma = 180^{\circ} because they form a straight angle. But \alpha + \beta + \gamma is the sum of the interior angles of a triangle. Therefore, the sum of the interior angles of a triangle is 180^{\circ}.

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