Triangle Inequality Theorems in One, and Two Triangles.

What is needed to do in order to find out if three line segments will form a triangle, or not? How may you order the sides of a triangle, if you know the angles? How may you order the angles, if you know the sides? If you have two triangles with two corresponding pairs of congruent sides, how do you know which one has the greatest angle included to those two sides? or the largest side opposite to the included angle?

This lesson starts with simple steps showing you the triangle inequality theorems in one triangle, and then it moves to triangle inequality in two triangles. In the process you are given examples, and suggested problems to test your understanding. Go for it! After most of the examples; you will be presented with a suggested problem to solve, you will be able to solve it on the screen with your stylus and the marker tools menu.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

Included angle
The angle made by two consecutive sides of a polygon.

Included side
The side between two consecutive angles in a polygon.

A polygon is a two-dimensional geometric figure with these characteristics: 
It is made of straight line segments.
Each segment touches exactly two other segments, one at each of its endpoints. 
It is closed -- it divides the plane into two distinct regions, one inside and the other outside the polygon.

Side of a polygon
A single segment from the union that forms a polygon.

A polygon with three sides.

Triangle inequality
The triangle inequality says that for three lengths to make a triangle, the sum of the lengths of any two sides must be greater than the third length.


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