Quadrilaterals and "n"-gons - Sum of Its Interior Angles
Warm Up
What is the interior angle sum of any triangle?
We will be exploring what the sum of the interior angles of any quadrilateral will be.
Explore the app below to move the vertices of the quadrilateral to make different kinds of quadrilaterals. Take note of the sum. Does it ever change?
Let's explore the why....
You should notice that the sum of any quadrilateral is 360 degrees. Now we'll see why this holds and extend that reasoning to find angle sums of other shapes...
Use this for the instructions that follow.
Using the "Polygon" feature, construct another triangle that connects to the one above.
What shape did you just create?
Now use the "angle" feature to measure each of the four angles of your new quadrilateral. Add them up and see if they sum to 360 degrees!
You just made a quadrilateral using two triangles. How does this support that the interior angle sum of a quadrilateral is 360 degrees?
Consider the quadrilateral below that I constructed from two triangles.
Create a pentagon by forming a triangle that connect to the quadrilateral above. Make sure it's created so it doesn't look like another quadrilateral! The sides should be unique!
Use the angle tool to measure the all angles in your constructed figure. What is the sum of all your angles (a.k.a. the 5 angles of the pentagon)?
You just made a pentagon using three triangles. How does this support that the interior angle sum of a quadrilateral is 540 degrees?
The Big Idea!
Think about what you have worked with. A quadrilateral had an angle sum of 360 and used two triangles. Your pentagon had an angle sum of 540 and used three triangles.
So intuitively, if you can make non-intersecting triangles within a polygon, you can use that to determine what the angle sum should be!