# Postulate in Math: Definition & Example

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• 0:00 What Is a Postulate?
• 1:09 Examples: Operational…
• 2:17 Examples: Geometric…
• 3:41 Applications of Postulates
• 5:04 Lesson Summary

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Lesson Transcript
Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

In this lesson, we'll discuss the meaning of postulates in mathematics and explore some common examples. We'll also apply these postulates to solving some geometric problems.

## What Is a Postulate?

A postulate is a statement that is accepted without proof. Axiom is another name for a postulate. For example, if you know that Pam is five feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings are at least five foot one. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.

Conjectures are often confused with postulates. Conjectures are conclusions that we make based on things that we observe. For example, if from Sunday to Thursday, Sam usually had pancakes for breakfast, you'd be safe in assuming he'd have pancakes on Friday and Saturday. However, on Friday, Sam may just have oatmeal. While conjectures may need to be proven before they're accepted, postulates are givens and need no proof. Every mathematical theorem began as a conjecture or a postulate before they were tested and accepted as proven mathematical facts, such as the ones we'll explore below.

## Examples: Operational Postulates

The following are some postulates that apply to the four operations, including addition, subtraction, multiplication, and division. These postulates are also algebraic properties used to solve algebraic equations.

The Addition Postulate: If you have one apple and Sally has one apple, when you both add the same quantity to your existing number of apples, you'll still have the same number of apples. Using algebra, the postulate states:

If x = y, then x + 4 = y + 4

The Subtraction Postulate: If you have ten apples and Sally has ten apples, when you both subtract the same quantity of apples from your existing number of apples, you'll still have the same number of apples.

If x = y, then x - 3 = y - 3

Without being repetitive, these same principles apply to both multiplication and division.

The Multiplication Postulate: If x = y, then x * 3 = y * 3

The Division Postulate: If x = y, then x / 7 = y / 7

## Examples: Geometric Postulates

Geometric postulates can help us solve problems with lines, line segments, and angles. Let's see what they say.

The Ruler Postulate: Points on a line can match up with real numbers. In other words, each point on the line will represent a real number.

The Segment Addition Postulate: Remember that a segment has two endpoints. If you have a line segment with endpoints A and B, and point C is between points A and B, then AC + CB = AB.

The Angle Addition Postulate: This postulates states that if you divide one angle into two smaller angles, then the sum of those two angles must be equal to the measure of the original angle. Formally, if ray QS divides angle PQR, then the measure of the angles PQS, plus the measure of angle SQR, is equal to the measure of angle PQR.

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