• Unit 3: Triangles, Congruence, and Other Relationships

    Making sure that objects are of equal size is important in life. Whether pieces of furniture, automobiles, or just pieces of a candy bar shared between siblings, we often have to make sure objects are the same size and shape.

    Have you ever had to prove something to a child? Sometimes, the best way to do that is to give the child a series of logical statements and then show how it all summarizes to one conclusion. In this unit, you will focus on showing that two triangles are identical. There are different methods to doing this, and the one you use will depend upon the information you have available to you. It is nothing more than following a series of logical statements and then showing how the statements draw a conclusion.

    In this unit, you will also learn more about triangles and their various parts. Triangles, believe it or not, are used more often in life than you might think. Triangles are often used to estimate distances. The process of triangulation has been used for over two thousand years; with this technique, we can use two known locations and determine the distance to a location that we can see but cannot necessarily get to, like a boat out in a lake. Today, we use triangulation for navigating boats, surveying land, launching model rockets, and other activities.

    We can also use triangles to map things out. For example, city planners often use the circumcenter of a triangle, which is a point in the middle that is equally distant from all three sides. They might use this to determine the location of a major parking garage, so that it is the same distance from three different companies, or they might want to make sure that a city monument is in the middle of a town plaza.

    If you live in a house, triangles are right over your heads. Construction workers use the midsegment of a triangle to help strengthen roof trusses when they build. If the truss is not supported properly, it could collapse, leading to lots of problems for the poor homeowner.

    Completing this unit should take you approximately 17 hours.