# Geometrical Proofs & Theorems

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### Using If-Then Logic

Every geometry proof is a sequence of deductions that use if-then logic. You write one of the given facts as statement 1. Then, for statement 2, you put something that follows from statement 1 and write

### Working with Definitions, Theorems, and Postulates

Definitions, theorems, and postulates are the building blocks of geometry proofs. With very few exceptions, every justification in the reason column is one of these three things. The below figure shows

### How to Prove Angles Are Complementary or Supplementary

Complementary angles are two angles that add up to 90°, or a right angle; two supplementary angles add up to 180°, or a straight angle. These angles aren’t the most exciting things in geometry, but you

### Using Addition Theorems in Proofs

There are four addition theorems: two for segments and two for angles. They are used frequently in proofs.

Use the following two addition theorems for proofs involving three segments or three angles:

### Using Subtraction Theorems in Proofs

There are four subtraction theorems you can use in geometry proofs: two are for segments and two are for angles. Each of these corresponds to one of the addition theorems.

### Using Theorems of Like Multiples and Like Divisions in Proofs

The Multiplication and division theorems are based on very simple ideas, but they do trip people up from time to time, so pay careful attention to how these theorems are used in the example proofs.

### Proving Vertical Angles Are Congruent

When two lines intersect to make an X, angles on opposite sides of the X are called vertical angles. These angles are equal, and here’s the official theorem that tells you so.

### The Components of a Proof

A two-column geometry proof is a problem involving a geometric diagram of some sort. You’re told one or more things that are true about the diagram (the

### The Transitive and Substitution Properties

You’re probably already familiar with the Transitive Property and the Substitution Property from algebra. If a = b and b = c, then a = c, right? That’s transitivity. And if

### Proof Strategies Summarized

The following strategies can help you a great deal when you’re working on two-column geometry proofs. You should review these strategies and practice using them until they become internalized. These strategies