2-5 Postulates & Proofs

• postulate: a conditional statement in Geometry that makes total sense and is automatically accepted as true…

“Through any two points, there is a line”

“Through any three points not on a line, there is a plane”

…wait, there’s more…

“A line contains at least TWO points”

“A plane contains at least three non-collinear points”

“If two points lie in a plane, then their whole line is in that plane”

“If two lines intersect, then their intersection is exactly one point”

That’s a converse, remember?

That’s a converse, too

Lil’ WayneSez

If you see somethin’ in Geometry, and

youare like, “Well, No

Duhh!”, it’s probably a

postulate.

We use postulates to determine the truthfulness of statements in Geometry.

EXAMPLE: If points A, B, and C lie in plane M, then they are collinear.

ALWAYS SOMETIMES NEVER

You can use postulates to PROVE things in Geometry.

A proof is a list of statements you make supported by postulates.

Once you PROVE a statement with postulates, it becomes a theorem.

And then, once you got a theorem, you can use it in other proofs.

To Write a “Proof”1. Write what is being proved

2. Write what is “given”

3. Try to draw a picture

4. Organize your thoughts and statements with postulates untilyou get to the end.

Given M is the midpoint of CD, prove to me that

CM = MD.~