Geometry Essentials For Dummies

Chapter 12

Ten Big Reasons to Use in Proofs

IN THIS CHAPTER

Segment and angle postulates and theorems

Parallel-line theorems

Triangle definitions, postulates, and theorems

Here’s the top ten list of definitions, postulates, and theorems that you should absotively, posilutely know how to use in the reason column of geometry proofs.

The Reflexive Property

The Reflexive Property says that any segment or angle is congruent to itself. You often use the Reflexive Property, which I introduce in Chapter 5, when you’re trying to prove triangles congruent or similar. Be careful to notice all shared segments and shared angles in proof diagrams. Shared segments are usually pretty easy to spot, but people sometimes fail to notice shared angles.

Vertical Angles Are Congruent

The vertical angle theorem isn’t hard to use, as long as you spot the vertical angles (see Chapters 1 and 2). Remember — everywhere you see two lines that come together to make an X, you have two pairs of congruent vertical angles (the ones on the top and bottom of the X and the ones on the left and right sides of the X).

The Parallel-Line Theorems

There are ten parallel-line theorems that involve a pair of parallel ...