Postulates+5-11

Laura Dobens
 * Postulate 5:** Through any two points there exists exactly one line

Where two points exist you can draw a straight line through them Can you draw a line through this point?
 * No, you must have two points to make a line**

In the figure above the line contains 3 colinear points, is it a line?
 * Postulate 6:** A line contains at least two points

Yes, as long as the three points are collinear you can draw a straight line through them

Kristin T.
 * Postulate 7:** If two lines intersect, they intersect at exactly one point.



In the above diagram, Point S is the intersection of line MN and line LK.

Here are some practice problems:



Do the above lines intersect?


 * No, they do not. There is no point indicating that the two lines intersect.**



Do the above lines intersect?


 * Yes, they do. There is a point indicating that the lines are intersecting.**


 * Postulate 8:** Through any 3 non-collinear points, there exists exactly one plane.

In the following figure, there are 3 non-collinear points, which makes the figure a plane.

Here are some practice problems with planes:



Is the above figure a plane?

No, the figure is not a plane because all three 3 points are on the same line.


 * Postulate 10**: If two points lie in a plane, the line containing the points also lies in the plane.

-Line k contains points A and B, and also lies in the plane. -Plane A and Plane B interesect through several lines: line n, line q, line c, and line w. Meaghan Coble =**Postulates 5-11**= Miranda J. Kathleen D. Danielle C. Rachel S.
 * Postulate 11:** When two planes intersect, they intersect at a line.

Postulate 5: Angle Addition Postulate: If D is in the interior of angle ABC, then measure of angle ABC = measure of angle ABD + measure angle DBC. 

MEvery angle, except a straight angle, has exactly one bisector.

Question: Bisect this angle



answer:

Postulate 7: If two lines intersect, then their intersection is exactly one point



Line BI intersects line AC at point A and line BI intersects line HF at point D

Question: How do you know that line BI intersects the two horizontal lines?

Answer: the point A and point D are created

Postulate 8:

Postulate 9: A plane contains at least three non collinear points.

What three points are noncollinear?

Answer: Points C, B, E

Postulate 10: If two points lie in a plane, then the line containing them lies in the plane.

Points K and L lie on the same line which both lie in the same plane.

Postulate 11 States that:

If two planes intersect, then their intersection is a line

> Practice Problem: > Identify the intersection betwee n two planes. > > **Choices:** > A. Plane A > B. Plane B > C. Line CD > D. None of these > > > **Correct Answer: C** > **Solution:** > **Step 1:** Two planes are said to be in intersection if they cross in a single line. > **Step 2:** Here, line CD intersects the plane A and plane B shown in figure. > **Step 3:** Therefore, line CD is the intersection between the two planes.