## Day 98 – How Many Triangles Can Fit Inside?

After a quick review on quadrilaterals using Kahoot, we moved on to our next topic.

The goal today was for students to use triangles on the Smartboard to figure out how many triangles will fit inside different polygons.

We started with one triangle (180 degrees).

How many triangles can fit into one quadrilateral?   By dragging and rotating the triangles, students found that 2 would fit inside.

4 sided figure –>

2 triangles —>

2 x 180 = 360 degrees.

Next was the pentagon.  Several students came up to the board to attempt drawing in the triangles in different ways.  Each time, we came up with 3 triangles.

5 sided figure –>

3 triangles –>

3 x 180 = 540 degrees.

Anyone noticing a pattern…?  Many students were.

The hexagon was next.  4 triangles could fit inside a hexagon.  6 sided figure –>

4 triangles –>

4 x 180 = 720 degrees.

I think we’re on to something….

I asked the students to predict the number of triangles that would occur in an octagon.  (6!!!)  But still, we tested it out to be sure.  Sure enough 6 was right, and sure enough they had figured out the formula for determining the sum of interior angles of a polygon.

They stated it perfectly,

“To find the number of triangles in a polygon, take the number of sides and subtract 2.”

But wait…this only gives us the number of triangles.  How does that help us find the sum of interior angles?

“Multiply that number by 180!”

They got it.  This led us to some practice which included regular and irregular shaped polygons, all of which used the same rule to find the sum of interior angles.