What if you wanted to classify the Bermuda Triangle by its sides and angles? You are probably familiar with the myth of this triangle; how several ships and planes passed through and mysteriously disappeared.
The measurements of the sides of the triangle from a map are in the image. What type of triangle is this? Using a protractor, find the measure of each angle in the Bermuda Triangle. What do they add up to? Do you think the three angles in this image are the same as the three angles in the actual Bermuda triangle? Why or why not? After completing this Concept, you'll be able to determine how the three angles in any triangle are related in order to help you answer these questions.
CK-12 Foundation: Chapter4TriangleSumTheoremA
James Sousa: Proving the Triangle Sum Theorem
In polygons, interior angles are the angles inside of a closed figure with straight sides. The vertex is the point where the sides of a polygon meet.
Investigation: 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, ∠1,∠2, and ∠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?
1. △ABC above with AD←→ || BC¯¯¯¯¯¯¯¯
Alternate Interior Angles Theorem
≅ angles have = measures
Linear Pair Postulate
Angle Addition Postulate
There are two theorems that we can prove as a result of the Triangle Sum Theorem and our knowledge of triangles.
Theorem #2: The acute angles in a right triangle are always complementary.
Show why Theorem #1 is true.
Use the picture below to show why Theorem #2 is true.
Watch this video for help with the Examples above.
CK-12 Foundation: Chapter4TriangleSumTheoremB
Concept Problem Revisited
The angle measures in the picture are the measures from a map (which is flat). Because the earth is curved, in real life the measures will be slightly different.
A triangle is a three sided shape. All triangles have three interior angles, which are the inside angles connecting the sides of the triangle. The vertex is the point where the sides of a polygon meet. Special types of triangles are listed below:
Scalene: All three sides are different lengths.
Isosceles: At least two sides are congruent.
Equilateral: All three sides are congruent.
Right: One right angle.
Equiangular: All three angles are congruent.