1. 1.1Points, Lies, and Planes Warm Up Simplify Each Expression.
3x – 5 + 7x y – 12y (x – 3) – 24
m + 6(2m – 12) (2p – 8) – 4(8p – 7)

2. 1.1Points, Lies, and Planes Objectives
Identify, name, and draw points, lines, segments, rays, and planes.
Apply basic facts about points, lines, and planes.

3. Definition – Uses __________ words to describe a ________ word.

4. Three Undefined Terms Description
Point has _____ dimension. It is usually represented by a _______ ________
Line extends in _____ dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in ______ ___________
Plane extends in _____ dimensions. It is usually represented by a shape that looks like a tabletop or wall. Your must imagine that the plane extends __________ _____, even though the drawing of a plane appears to have edges.
Name
Picture

5. Description
Collinear points are ________ that lie on the same _________.
Coplanar points are __________ that lie on the same ____________.
Picture

6. Example 1
Name a point
Name a line
Name a plane
Name three points that are collinear.
Name three points that are not collinear
Name four points that are coplanar
Name four points that are not coplanar

7. Between a point is between two other points if the three points are _______________. Intersect – to have one or more __________ in common. Intersection - the set of ___________ that two or more geometric figures have in ___________.

8. Description
Line Segment (Segment) Part of a line that consists of ______ points, called endpoints, and all points on the line that are between the ________________.
Ray Part of a line that consists of a ________, called an initial point, and all points on the line that extend in _______ direction.
Opposite Rays If C is ___________ A and B, then 𝐶𝐴 and 𝐶𝐵 are opposite rays.
Name
Picture

9. c. Name the intersection of plane N and plane T.
Example 2
Name two opposite rays.
b. Name a point on 𝐵𝐶 .
c. Name the intersection of plane N and plane T.

10. Example 3
Draw three noncollinear points, J, K, L. Then draw 𝐽𝐾 , 𝐾𝐿 , and 𝐿𝐽 .
b. opposite rays with a common endpoint T c. 𝑄𝑅 and 𝑆𝑇 that intersect at point M.

11. Example 4
Draw and label each of the following.
a figure that shows a line that lies in a plane b. a figure that shows 𝐴𝐵 intersect plane S at point C.

12. Line Pairs
Description
Parallel lines – ____________ lines that do not ______________
Perpendicular Lines – two lines that ____________ to form ____________ angles.
Intersecting Lines – Lines that _________.
Skew Lines - ______ ____________ lines that do not _______________
Name
Picture

13. Example 5
Identify each of the following.
a. a pair of parallel segment
b. a pair of skew segments
a pair of perpendicular segments
What do you notice about all of the intersecting lines in this picture?
Draw a new picture where this is not true.