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?
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,
- 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?
||Alternate Interior Angles Theorem|
||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.
Proving Theorem #1
Show why Theorem #1 is true.
Proving Theorem #2
Use the picture below to show why Theorem #2 is true.
Bermuda Triangle 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.
To view the Review answers, open this PDF file and look for section 4.1.