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# Points , Lines and Planes - PowerPoint PPT Presentation

Points , Lines and Planes. Objectives : To identify and model points, lines , and planes To identify collinear and coplanar points and intersecting lines and planes in space. Definitions.

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### Points, Lines and Planes

Objectives:

To identify and model points, lines, and planes

To identify collinear and coplanar points and intersecting lines and planes in space.

• Point: a basic undefined term of geometry. A point is a location. In a figure, points are represented by a dot. Points are named by capital letters.

• Line: A basic undefined term of geometry. A line is made up of points and has no thickness or width. In a figure, a line is shown with an arrowhead at each end. Lines are usually named by lowercase script letters or by writing capital letters for two points on a line, with a double arrow over the pair of letters.

• Plane: A basic undefined term of geometry. A plane is a flat surface made up of points that has no depth and extends indefinitely in all directions. In a figure, a plane is often represented by a shaded, slanted 4-sided figure. Planes are usually named by a capital script letter or by three non-collinear points on the plane.

• Collinear: Points that are on the same line.

• Coplanar: Points that are on the same plane

• Undefined term: Words, usually readily understood, that are not formally explained by means of more basic words and concepts. The basic undefined terms in geometry are point, line, and plane

• Space: A boundless 3-dimensional set of all points.

• “A location”

• Represented by a dot

• Named with a capital letter!

• Can be referred as:

A or point A

• Has no thickness

A

• A string of points extending infinitely in two directions

• Has arrowheads on both ends.

• Named with a lower case letter…

• Named b or line b

• …Or with any TWO points on the line with a double headed arrow above it.

• Named AB or BA

• b

A

B

• Give 6 Possible names for the line:

• AB, BA, BC, CB, AC, CA

• List all possible names for the line:

• WX, XW, WY, YW, WZ, ZW, XY, YX, XZ, ZY, YZ, ZY

• Name the line:

• d

C

B

A

W

Y

X

Z

d

B

C

A

• A, B, and C are said to be:

• Collinear

• Are A, B, and D collinear?

• No

• D

A

D

• A “flat surface”

• Represented by a parallelogram

• Name by a capital letter; or 3 non-collinear points.

• Plane A or Plane BCD

• Has no thickness

C

B

A

D

• Name the plane with 1 letter:

• Plane A

• Name the plane by its points:

• Plane BCE

• Are B, C, E collinear?

• No

• Are B,C,D, and E coplanar?

• Yes

• Are B, C, D, and F coplanar?

• No

C

B

• E

• F

D

A

How many planes appear in this figure?

- 4; Plane FDG, Plane FED, Plane FEG, Plane T

Name 3 collinear points:

- A, B, C

Are points B, E, G, and D coplanar? Explain:

- No, D is not on plane T whereas B, E and G are on plane T.

Where does AC intersect Plane T?

- At B.

E

B

G

F

T

C