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Section 1.3Points, Lines, and Planes

LEARNING TARGETS:1. Students will be able to

identify and draw points, lines, planes, rays, and segments.

2. Students will be able to determine if points are collinear or coplanar.

VOCABULARY:- Undefined Term- Point, Line, Plane- Postulate- Collinear, Coplanar- Segment- Ray- Endpoint

+INTRODUCTIONThe legs of the tripod touch the table at three points. The legs suggest lines, and the table surface suggests a plane.

+Undefined Terms

Geometry depends on a common understanding of terms such as point, line, and plane.

Because these terms cannot be mathematically defined using other known words, they are called undefined terms.

+VocabularyPoints

A point has no dimension. It is represented by a small dot.

+Line

A line has one dimension. It extends without end in two directions. It is represented by a line with two arrowheads

+PlaneA plane has two dimensions. It is represented by a shape that looks like a floor or wall. You have to imagine that it extends

+Vocabulary

You need two points to describe a line.

You need three points to describe a plane.

+

POSTULATES:

Statements that are accepted without further justification.

+POSTULATE 1

Two points determine a line.Words:Through any two points there is exactly one line.

SymbolsLine n passes through points P and Q.

+POSTULATE 2Three Points Determine a Plane

Words:Through any three points not on the same line there is exactly one plane.

Symbols:Plane T passes through points A, B, and C.

+Example (In Notes)Use the diagram at right for #1-3.

Name four points. ____, ____, ____, ____ Name two lines. _______, _______

Name two planes. _____________, _______________

+Example 1 (From Book)

Use the diagram at the right.

Name three points.

Name two lines.

Name two planes.

+VocabularyCollinear PointsPoints that lie on the same line.

Coplanar PointsPoints that lie on the same plane.

Coplanar LinesLines that lie on the same plane.

+Example 2 (From Book)

Use the diagram at the right.

Name three points that are collinear.

Name four points that are coplanar.

Name three points that are not collinear.

+CHECK POINT

Use the diagram at the right. Name two lines. Name two planes. Name three collinear points. Name three noncollinear points. Name four coplanar points. Name two coplanar lines.

+Lines, Segments, and Rays

+ExampleDraw three noncollinear points, R, S, and T.

Then draw line RS.Then draw line segment ST.Then draw ray TR.

+Daily Puzzler

Draw three different planesthat intersect in one point.

+HOMEWORK

Page 17: #15-37 all, 38-52 even, 54-62 all, 66-72 all

Due Friday, 09/30Reminder: Quiz tomorrow