Lesson 4Postulates and Theorems About Points, Lines, and Planes

Postulate 5Through any 2 points there is exactly one line.

Theorem 4-1If two lines intersect, then they intersect at exactly one point.

Postulate 6Through any three noncollinear points there exists exactly one plane.

Theorem 4-2If there is a line and a point not on the line, then exactly one plane contains them.

Theorem 4-3It two lines intersect, then there exists exactly one plane that contains them.

Postulate 7If two planes intersect, then their intersection is a line.

Postulate 8If two points lie on a plane, then the line containing the points lies in the plane.

Postulate 9A line contains at least 2 points. A plane contains at least 3 noncollinear points. Space contains at least 4 noncoplanar points.

Space is made up of all possible planes, lines, and points. It extends indefinitely in all directions.3-Dimension

ExamplesMany problems on today’s lesson will pose a question and you will need to answer that question with an explanation (usually a postulate and/or theorem)

So be aware of which questions need explanation, because no credit will be given without one, especially yes/no or true/false

Example 1How many lines can you trace a path from point F to G?

Example 1How many lines can you trace a path from point F to G?One, Postulate 5Through any 2 pt. there is exactly one line.

Example 1How many lines can you trace a path from point F to G?One, Postulate 5Through any 2 pt. there is exactly one line. All other paths are not lines

Example 2How many planes exists in these 4 noncollinear points? Identify all planes and explain.4 PlanesPlanes WXY, WXZ, WYZ, and XYZPostulate 6

Ex 2 (extended): ApplicationProfessional photographers often use a tripod to hold their cameras steady. Explain why a quadripod is never used.Post. 63 noncollinear pts. will always find a plane. 4 points may cause the camera to wobble

Questions/ReviewBe prepared to draw and identify intersections of other figures.Read each question carefullyOften they will appear to be post/thms, but keywords will be left outFor example:

Do 4 points define space?

No, they must be noncoplanar points