1.2 Points, Lines, Planes, and Space Objectives -define lines, points, space, planes -Identify properties of collinearity -define postulate -identify postulates

B C A Point These are point A, point B, and point C A point is a location in space, that has no size but is represented by a dot labeled with a capital letter. B C A These are point A, point B, and point C When we talk about points in sentence form it is not always necessary to use the word “point” if we see just a CAPITAL letter it is understood that it is a point.

Space is the collection or set of all points.

All other geometric figures are made from an infinite set of points. The easiest way to think of these is that a point, though it has no size can be represented as a dot from your pencil, if you strung out an infinite amount of dots you soon get an image to appear.

m C A Lines The arrows show that the line extends forever A line is a series of points that extends without end in two (2) directions. The arrows show that the line extends forever A line is always straight (no bends/curves/corners) A line is represented by either a script lower case letter, or by 2 points on that line. So in words this would be line m or line AC. The symbol for a line AC would be m C A

If we take a line and break it up into parts, each part can be defined as a figure. If the part has two endpoints then it is a segment. Segments are labeled the same way as a line is, but the symbol displays 2 endpoints NOT ARROWS A B C A C

A C Points A and C are called endpoints In symbols it would be AC or CA A C

A B C This would be called AC If the part has one endpoint, and the other end extends forever it is called a ray. A B C This would be called AC Since A is the only endpoint, it has to be the first letter when naming the ray

Here we have what are called opposite rays, NAME THEM. Q

Name this line 4 different ways X m B R

C B A Collinear Points A, B, and C are collinear points Two or more points that all lie on the same line. C B A A, B, and C are collinear points

Are R, B, and C collinear? R C B A V

Noncollinear points are points that do not lie on the same line. So what are they? Noncollinear Noncollinear points are points that do not lie on the same line.

Plane A plane is a flat surface that extends without end in all directions. Think of a table top extending forever or a wall extending forever A plane can be represented by a single script UPPERCASE letter or by three (3) noncollinear points.

Q R T E This is plane R, or plane EQT

With what we know about collinear points and noncollinear points Define coplanar points… Define noncoplanar poits…

The Intersection of figures, is the point or group of points that both figures have in common.

Postulate A postulate is a statement that we have to accept as being true without any proof. DO NOT REMEMBER POSTULATES BY THEIR NAME(ex. Postulate 1.2), REMEMBER THEM BY THEIR STATEMENT

Homework Section 1.2 in MathXLforSchool.com