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Points , Lines and PlanesPowerPoint Presentation

Points , Lines and Planes

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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.

Definitions

- 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.

Definitions (continued)

- 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.

Point

- “A location”
- Represented by a dot
- Named with a capital letter!
- Can be referred as:
A or point A

- Has no thickness

A

•

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

- 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

- Named AB or BA

b

A

B

Name the Lines

•

- 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

Understanding Points and Lines

B

C

A

- A, B, and C are said to be:
- Collinear

- Are A, B, and D collinear?
- No

•

•

•

• D

Planes

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

Understanding Planes

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

Interpret Sketches

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

•

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