Name: Introduction to Geometry: Points, Lines and Planes

Euclid: “What’s the point of Geometry?- Euclid” http://www.youtube.com/watch?v=_KUGLOiZyK8&safe=active

 When do historians believe that Euclid completed his work?

 What key topic did Euclid build on to create all of Geometry?

 What is an axiom?

 Why do you think that Euclid’s ideas have lasted for thousands of years?

*Point – is a ______in space. A point has ___ dimension. A point is name by a single capital letter. (ex)

*Line – consists of an ______number of points which extend in ______directions. A line is ___-dimensional. A line may be named by using a single lower case letter OR by any two points on the line. (ex)

*Plane – consists of an ______number of points which form a flat surface that extends in all directions. A plane is _____-dimensional. A plane may be named using a single capital letter OR by using three non- collinear points. (ex)

*Line segment – consists of ____ points on a line, called the endpoints and all of the points between them. (ex)

*Ray – consists of ___ point on a line (called an endpoint or the initial point) and all of the points on one side of the point. (ex)

*Opposite rays – share the same initial point and extend in opposite directions on the same line.

*Collinear points –

(ex)

*Coplanar points –

(ex)

*Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of elements that the figures have in common.

Pair-Share:

Def: Postulate or Axiom:

(ex) One rule in soccer is that ______.

Point, Line and Plane Postulates *Postulate 1-1-1: Through any two points there exists exactly one line

*Postulate 1-1-2: Through any three noncollinear points there exists exactly one plane containing them.

*Postulate 1-1-3: If two points lie in a plane, then the line containing them lies in the plane

*Postulate 1-1-4: If two lines intersect, then their intersection is exactly one point

*Postulate 1-1-5: If two planes have points in common, the set of intersection points is either a line or a plane.

Determine which postulate goes with each statement. Use the diagram to help you!

1.The points X, Y and Z lie in a plane (labeled B).

2. The points X and Y lie on a line labeled m.

3. The planes A and B intersect in a line labeled l

4.The points X and Y lie in plane B. Therefore line m lies in plane B.

Practice:

1. Draw three noncollinear points and label them A, B, and C. Then draw point D on AB between points A and B.

2. Are points A, B and D collinear? Are points B, C and D collinear?

3. Are CA and CB opposite rays? Are DA and DB opposite rays?

4. True or false: AB has a definite length and thickness.