http://www.ck12.org Chapter 4. Triangles and Congruence
Triangle Sum Theorem
Interior Angles(in polygons): The angles inside of a closed figure with straight sides.
Vertex:The point where the sides of a polygon meet.
Triangles have three interior angles, three vertices and three sides.
A triangle is labeled by its vertices with a 4 .This triangle can be labeled 4 ABC, 4 ACB, 4 BCA, 4 BAC, 4 CBAor
4 CAB. Order does not matter.
The angles in any polygon are measured in degrees. Each polygon has a different sum of degrees, depending on the
number of angles in the polygon. How many degrees are in a triangle?
Investigation 4-1: Triangle Tear-Up
Tools Needed: paper, ruler, pencil, colored pencils
- Draw a triangle on a piece of paper. Try to make all three angles different sizes. Color the three interior angles
three different colors and label each one,^61 ,^62 ,and^6 3. - Tear off the three colored angles, so you have three separate angles.
- Attempt to line up the angles so their points all match up. What happens? What measure do the three angles
add up to?
This investigation shows us that the sum of the angles in a triangle is 180◦because the three angles fit together to
form a straight line. Recall that a line is also a straight angle and all straight angles are 180◦.