1.1Points, Lies, and Planes

Warm Up

Simplify Each Expression.

1. 3x – 5 + 7x 2. 5y – 12y + 8 3. 4(x – 3) – 24

4. -8m + 6(2m – 12) 5. 3(2p – 8) – 4(8p – 7)

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Objectives

Identify, name, and draw points, lines, segments, rays, and planes.

Apply basic facts about points, lines, and planes.

1.1Points, Lies, and Planes

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Definition – Uses __________ words to describe a ________ word.

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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

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Description

Collinear points are ________ that lie on the same _________.

Coplanar points are __________ that lie on the same ____________.

Picture

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Example 1a. Name a point

b. Name a line

c. Name a plane

d. Name three points that are collinear.

e. Name three points that are not collinear

f. Name four points that are coplanar

g. Name four points that are not coplanar

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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 ___________.

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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 and are opposite rays.

Name

Picture

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Example 2

a. Name two opposite rays.

b. Name a point on

c. Name the intersection of plane N and plane T.

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Example 3

a. Draw three noncollinear points, J, K, L. Then draw , , and .

b. opposite rays with a common endpoint T. c. and that intersect at point M.

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Example 4

Draw and label each of the following.

a. a figure that shows a line that lies in a plane. b. a figure that shows intersect plane S at point C.

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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        

Line Pairs

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Example 5

Identify each of the following.

a. a pair of parallel segment

b. a pair of skew segments

c. 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.