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Author:
Rachel Kaplan

To understand:

-points

-lines

-planes

-axioms/postulates

-theorems

In this learning packet, we will define the basic terms used in geometry and provide examples.

Tutorial

` `**Postulates**
A) Through any two points, there is exactly one line.
B) Dimension Assumption: Given a line in a plane, there exists a point in the plane not on that line.
C) If two points lie on a plane, the line containing them also lies on the plane.
D) Through three noncolinear points, there is exactly one plane.
E) If two different planes have a point in common, then their intersection is a line.

```
F) A line segment can be extended indefinitely along a line.
```

` `

**Theorems**

**A)** Two different lines intersect in at most one point.

**B)** If C is between A and B and on , then AC + CB = AB.

Related Theorems:

**C)** If A, B, and C are distinct points and AC + CB = AB, then C lies on .

**D) Pythagorean Theorem:** a^{2} + b^{2} = c^{2}, if c is the hypotenuse.

**Note:** While you can usually get away with not knowing the names of theorems, your Geometry teacher will generally require you to know them.