Angle Relationships

The angle relationships that we have encountered so far are supplementary angles, corresponding angles, alternate interior angles, same side exterior angles, alternate exterior angles, and same side interior angles.

Angles in a Triangle

The sum of the angles of ANY triangle equals 180 degrees. For example, if there is a right triangle like the one below and you are trying to find X, all you have to do is add the sides that you do know together (66+39). Then, you subtract that number from 180 (180-105). Then your answer is 75. To check your answer, you add 66+39+105 which equals 180.

Triangle Inequality

The corners of a triangle have to be able to touch. The ones that did not form triangles don’t touch corners but the ones that did do touch corners. Three side lengths WILL NOT make a triangle if its corners cannot touch. Three side lengths WILL make a triangle if the the corners can touch properly.

Triangle Side-lengths Patterns

If 3 squares have sides that make and acute triangle, the sum of the areas of the two small squares will equal 180. If squares have sides that make and obtuse triangle, the sum of the areas of the two small squares will equal 180. If 3 small squares have sides that make a right triangle, the sum of the areas of the two small squares will be 180

Square Roots

A square root is the reverse of squaring a number. To estimate a square root you have to find what perfect square root it is closest to. Then you square it and which ever number is the closest to the original number, that is the approximate square root.

Pythagorean Therom

This theory can be used because if a right triangle is missing the hypotenuse, you can add together the area of the legs and then square root that. This will get you the length of the hypotenuse. To get the length of a leg, you add together the areas of the other two lines and them subtract the leg from the hypotenuse. You subtract that and then square root it. This gets you the length of a leg.