By drawing segments that connect vertex A to all the other vertices, we have broken up this quadrilateral into triangles! Now connecting point A to point B and then point A to point C didn't really do anything, since they were already connected. That means we were only able to draw in one line that wasn't already there. We call segment AC a diagonal of the quadrilateral.
1. What do you remember about the sum of the angles in a triangle?
The sum of the angles in a triangle add up to 180 degrees.
1. How many sides does a quadrilateral have?
3. How many triangles were you able to create in the quadrilateral above?
4. What might you guess then would be the sum of all the angles in a quadrilateral? (Use you answers from questions #1 and #3)
Since we know that all the angles in a triangle add up to[b] [color=#0000ff]180 degrees[/color][/b], and that we could create [color=#ff00ff][b]2 triangles[/b][/color] inside the quadrilateral above, the sum of all the angles inside a quadrilateral can be given by[br][br][center][math]180^\circ\times2=360^\circ[/math][/center]So the sum of the angles inside a quadrilateral must be 360 degrees.