Odyssey Geometry 2016-17

Chapter 5 Overview

This chapter will focus on presenting and proving relationships within a triangle that students can, in turn, use to prove relationships within other figures. Some of the relationships involve midsegments, angle bisectors, perpendicular bisectors, altitudes, medians, and inequalities. Students will learn how to form inverses and contrapositives, which prepares them to prove several theorems indirectly and provides another invaluable technique of proof.

Objectives:

• You will learn about geometric relationships within triangles. 
• You will learn about three lines that pass through one point and find the four sets of such lines that exist for every triangle. 
• You will learn about two other types of statements that are related to a conditional, as well as another type of reasoning—indirect reasoning. 
• You will apply indirect reasoning to deduce information about inequalities in triangles.