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The Building Blocks of Geometry

• Points

• Line

• Plane

Q: These terms are called undefined terms. Why?

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In geometry, definitions are formed using known words or terms to describe a new word.  A formal definition states what the term being defined is and how it differs from others like it. There are three words in geometry that are not formally defined, but there is an agreement about what they mean.  These three undefined terms are point, line and plane.

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Points

Point - a location in space. It has no size. It is named by a capital letter.

.A

Points are usually represented with a capital letter, but in the coordinate plane a point is represented as an ordered pair (x,y).

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Points

Can anyone identify examples of points in the real world?

Linesline - a series of points that extends in two opposing directions without end. Lines have no thickness.

Q S

Lines can be represented by two points on the line.

Example: QS or SQ

On the coordinate plane a line could be represented as an equation relating a set of points.

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Lines

Write the equation of a line through the points D(2, 9) and C(-3, 24). Also, represent it symbolically (not graphically).

Line SegmentsLine segment - a part of a line with two endpoints.

R B

A segment is named by its endpoints.

Example: RB or BR

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Line Segments

Why is a line segment a defined term if a line is considered undefined?

RaysRay - consists of an endpoint and all the points of a line on one side of the endpoint.

C D

Read it as: “Ray CD” (the order does matter)

Write it as:

CD

True or false, ray NQ has another name. If true, what is the name?

Name a pair of opposite rays.

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Planesplane - a flat surface with no thickness that extends without end in all directions.

http://www.mathsisfun.com/geometry/plane.html

What is wrong geometrically with the .gif in the link above?

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Identify which of the following apply.

When two planes intersect, ____ line(s) are formed.

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1

2

3

Infinity

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True or False:If two lines do not intersect, then they are parallel.

If two lines are parallel, then they do not intersect.

If two lines intersect, then they are not parallel. Hint: Look for counterexamples (they fit the first part of the statement but not the second). 13

Planes

Intersecting lines - cross (intersect) at exactly one point.

Parallel lines – do not intersect, but on the same plane.

Skew lines – do not intersect, but are on a different plane.

• Collinear Points

• Coplanar points

• Opposite rays

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• Collinear Points - points that lie on the same line.

• Coplanar points - points that lie in the same plane.

• Opposite rays - 2 rays that lie on the same line, with a common endpoint and no other points in common. Opposite rays form a straight line and/or a straight angle (180°:).

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Congruent SegmentsTwo segments are congruent if and only if they have equal lengths. You can show two segments are congruent by making identical markings.

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Group Investigation

With your partner…

Look around the classroom and identify examples of each of these terms: point, line, plane, line segment, congruent segments, midpoint of a segment, parallel line segments and ray.

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