THE SUM OF THE ANGLES OF A TRIANGLE (Part 1: Exploration)

Monday, June 24, 2013

mathematics,geometry,angles,triangles,IGCSE

Everybody knows that the sum of the measures of the angles of any triangle is 180 degrees. If I may ask each one of you why, one of the reasons that I may probably hear is that "Our math teacher told us!" - which should not be the case. You should know how to show that the sum of the angles of any triangle is really 180 degrees. Where do 180 degrees come from? Why 180 degrees? Why not 360 degrees?

The purpose of this post is to show you how to prove that the sum of the angles of any triangle is really 180 degrees. This is the first method, which is the elementary way - the easiest way, to prove it. The other methods will also be posted here.

PROVE: The sum of the measures of the angles of any triangle is 180 degrees.

PRE-REQUISITE: The sum of the measures of the angles that form a straight line is 180 degrees.

MATERIALS NEEDED: colored papers or cardboards, pair of scissors, ruler, marker

PROCEDURES:

1. Cut three different types of triangles, classified according to angles. Use the colored papers or cardboards for the triangles. One should be a right triangle, another should be an acute triangle and the last should be an obtuse triangle.

mathematics,geometry,angles,triangles,90 degrees,IGCSE

2. For us to easily identify the angles of the triangles later, highlight the edges of each triangle using a black (or any dark colored) marker.

mathematics,geometry,triangles,angles,IGCSE

3. Using a pair of scissors or cutter, cut the sector/region of the angles of each triangle.

mathematics,angles,triangles,geometry,IGCSE

4. For each of the triangles, arrange the regions of the angles in such a way that they are adjacent to each other. Notice that in this case, the lower part of the angles form a straight line.

5. In each of the figures formed, the angles formed a straight line at the bottom part. Recall that the sum of the angles that form a straight line is 180 degrees.

CONCLUSION: The sum of the measures of the angles of any triangle is 180 degrees.

For educators and parents, I have made a worksheet for this activity for your class/children. You are free to download and print it. You may group your students and let each group work on a triangle or all the triangles. I hope this will be helpful.

Your comments and suggestions are welcome here. Write them in the comment box below. Thank you!