 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 2, Part B:
 The triangle inequality is a famous result in mathematics. It says that for three lengths to make a triangle, the sum of any two sides must be greater than the third side. Often you will see a picture like this, where a, b, and c represent the three lengths of the sides. The triangle inequality is the mathematical statement of the old adage, "The shortest distance between two points is a straight line." If you don't travel along the straight line, you travel two sides of a triangle, and that trip takes longer. You have also probably found that triangles are rigid. That is, if a set of lengths makes a triangle, only one triangle is possible. You can't push on the vertices to make a different triangle with the same three sides. Triangles are the only rigid polygon, which makes them quite useful for construction. This property is often abbreviated as SSS (side-side-side) congruence. If the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent. That is, they have exactly the same size and shape. All of the angle measurements will match, as will other measurements, such as their areas, the lengths of the corresponding altitudes, and so on. If you cut the two triangles out from a piece of paper, you could fit one exactly on top of the other.   Session 2: Index | Notes | Solutions | Video