Chapter 2

Geometry Proof Starter Kit


Bullet Introducing if-then logic

Bullet Theorizing about theorems and defining definitions

Bullet Understanding the complementary and supplementary angle theorems

Traditional two-column geometry proofs are arguably the most important — and for many students, the most difficult — topic in a standard high school geometry course. In this chapter, I aim to declaw them! First, I give you a schematic drawing that shows you all the elements of a two-column proof and where they go. Then, I explain how you prove something using a deductive argument. After that, you’ll be ready for a starter kit of your first 18 theorems along with some proofs that illustrate how to use them. Before you know it, you’ll be a proof-writing crackerjack!

The Lay of the (Proof) Land

A geometry proof involves a geometric diagram of some sort. You’re told some things that are true about the diagram (the givens), and you’re asked to prove that something else is true (the prove statement). Every proof proceeds as follows:

  1. You begin with one or more of the given facts about the diagram.
  2. You state something that follows from the given fact or facts; then you state something that ...

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