Lesson 1.2

Intro to Geometry

Learning Target

I can understand basic geometric terms and postulates.

Points Points do not have actual size.

How to Sketch:

Using dots

How to label:

Use capital letters

A

B

Lines

Lines extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends.

How to name: 2 ways(1) small script letter – line n(2) any 2 points on the line -

Never name a line using three points - , , , , ,AB BC AC BA CA CB

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nA

BC

ABC�������������� �

A part of a line that consists of two endpoints and all the points in between them.

How to name: by 2 endpoints

Segments

AB C

A part of a line that consists of one endpoint and all the points to one side of that endpoint.

Rays

AB C

How to name: 2 points with ENDPOINT FIRST

Not like this…

Two rays that share the same endpoint and form a straight line.

Opposite Rays

AB C

Collinear Points

A B CA

B

C

Collinear Non collinear

Collinear points are points that lie on the same line.

Coplanar Objects

Coplanar objects (points, lines, etc.) are objects that lie on the same plane.

H

E

G

DC

BA

F

Are the following points coplanar?

A, B, C ?A, B, C, F ?H, G, F, E ?E, H, C, B ?A, G, F ?C, B, F, H ?

YesNo

YesYesYesNo

Postulates

An accepted statement of fact.

Line POSTULATE – Through any two points there is exactly ONE line

AB

Planes POSTULATE – Through any 3 non-collinear points there is exactly ONE plane

A plane is a flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 2 ways

(1) Capital script letter – Plane M(2) Any 3 non collinear points in the plane - Plane: ABC or BCA or

BAC, etc.

A

BC

M

Different planes in a figure:A B

CD

EF

GH

Plane BCG

Plane ABF

Plane CDH

Etc.

Other planes in the same figure:

Any three non collinear points determine a plane!

H

E

G

DC

BA

F

Plane ACG

Plane ACH

Etc.

Intersection of Two Lines POSTULATE

The intersection of two lines is a point.

m

n

PLine m and line n intersect at point P.

Intersection of Two Planes POSTULATE

P

R

A

B

Plane P and Plane R intersect at the line AB�������������� �

The intersection of two planes is exactly ONE line.