Geometry – Sum of all angles of a Triangle

Growing up, we learned in geometry that sum of all the interior angles of a triangle is 180 degrees. But can you illustrate it ?


Let’s find it out together. Cut any shape triangle from a piece of paper. Mark all the angles with different colors on both the sides. Orient the triangle so that the longest side is the base.

Measure the angles using protactor and write it at the corresponding vertices on both sides of the paper.

Mark the center point of the other two sides.

And fold the top vertices down at this midsection such that it touches the base.

Fold the other two vertices so that all three meet at the same point.

All the vertices meet at the straight line and we know that a straight line form a linear angle which is 180 degrees. Hence, we can proof that the sum of all the interior angles of a triangle is 180 degrees.

You can also tear the three corners of the triangle and line them up on a straight line to prove that their sum is equal to 180 degrees. And here is a short clip of how this blog post started :- )

I also want to recommend the two geometry books, we absolutely love. Art of Problem Solving Introduction to Geometry and Understanding Geometry.

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