Angle Sum Theorem

I've taught Angle Sum Theorem in the past but I felt as though my students didn't truly understand what it means or how it actually works.  They can tell you that all angles in a triangle add up to 180 degrees, but if you ask them how do you know it's true they couldn't give you a good reason.  I usually get the response of "because you told us it does".  UGH!  Not the response I'm looking for.

This year I was determined to find a way that would help them understand just how it worked, and I came across these two different methods.  I used BOTH.

The first method is where you give students three different triangles: Equilateral, Scalene, and Isosceles.  They color each of the angles in the triangle a different color and rip off the angles.  Then they have to join all three angles, and in the end they form a straight line which they know measures 180 degrees.

The second method we used is where each student again is given three different triangles: Equilateral, Scalene, and Isosceles.  They again color each of the angles in the triangle a different color.  They start off by folding the triangle to create an altitude. Then the top angle is folded down to the point where the altitude and base meet.  The two other angles fold in, showing all three angles lined up creating a straight line.

They liked the folding method because when they glued them into their ISN they were able to fold and unfold the triangle as many times as they want.  The ones that were ripped could only be done the one time.

Here are the left pages when they are finished.  

Unfolded Triangles

Folded Triangles

On the right side of their notebook we worked out several different types of problems involving the angle sum theorem.  We also revisited supplementary angles, vertical angles, as well as the different types of triangles and their characteristics.

Overall this page so far has probably been their favorite.  I succeeded in getting them to understand why the angles in a triangle add up to 180 degrees, and I no longer get answers of "because that's what you said".

Angle Sum Theorem(1)

Angle Sum Theorem Practice Problems Sheet