Interior Angles of a Triangle

The one thing all triangles have in common is that all interior angles of a triangle add up to 180°, no matter what type or size the triangle is. We also know that a straight line is 180°. A really great way to help your students understand this correlation is with this simple math activity. First, give each student a piece of paper about half the size of a piece of copy paper. I suggest you use colored copy paper since it makes the activity more fun (seriously, a table full of college students was fighting over the "best" color of paper to grab!) Next, give each student a ruler and tell them make and then cut out a triangle. Tell them they can make any type of triangle they want. Once each student has their triangles cut out, have them use their angle finders (explained in a previous blog post) to identify what type of triangle it is (acute - all angles less than 90°, right - one angle that is exactly 90°, or obtuse - one angle greater than 90° but less than 180°.) You can also have them identify their triangles by their sides (equilateral - all three sides are the same length, isosceles - at least two sides the same length, or scalene (all three sides are different lengths.)  

Now that the students have all constructed and identified their triangles, you are going to have them rip them up. Yes, you read that right. Tell them to rip each corner off of their triangles. This will be really hard for some to do (it was for me) but they need the angles to be separated for the activity to work. They HAVE to rip them off too, not cut them off, because you need the jagged edges to know exactly where the angles of their triangles are. If you cut them off you just have three mini triangles with three different angles and this activity will be a lot harder. Here is an example of my triangle with the corners ripped off.

After the students have ripped the corners off, have them arrange the pieces tip to tip like this

Each and every student, regardless of the type or size of their triangles, will all have made a straight angle (180°) when they arrange their corners (interior angles) tip to tip. This activity helps to drive home the fact that ALL triangles have the same sum of all of their interior angles no matter what each angle's individual measure is. Once the students know this, they can figure out the measure of angle x when given the measure of the two other angles. 

Once the students know how to figure out the measurements of the interior angles of a triangle, this activity also helps them when figuring out the measurements of the exterior angles as well. Because this activity also taught them that a straight line is 180°, students can extend any one side of the triangle to form a straight line and subtract the measurement of the supplementary interior angle from 180° to get the measurement of the exterior angle. This you tube video explains that concept in better detail. 

I hope you find this activity helpful. Try it out with your students and see if it works for you. Happy teaching! 😊