Lesson 1: (1.3) Points, Lines, and Planes

“Dogs have owners. Cats have staff.”

“Dogs feel very strongly that they should always go with you in the car, in case the need should arise for them to bark

violently at nothing right in your ear.”-Dave Barry

What are we learning?

Students will…• understand basic terms. • understand basic postulates of geometry.

Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a)

Purpose: Photographers and surveyors use a tripod or a three-legged stand for their instrument.

Terms

A point is a location. It does not have a size.Space is the set of all points.

A line is a series of points going in two opposite directions. You can name a line by any two points on the line.Points that lie on the same line are collinear (opposite: noncollinear).

A

B Name: AB or BA

A

B

C

Terms

A plane is a surface that has no thickness. It contains many lines going in all directions. A plane is named by one capital letter or at least three of its noncollinear points.

Points and lines in the same plane are coplanar.

Names:

P

Plane P Plane ABC or Plane BCA

cPostulates/Axioms

A postulate or axiom is an accepted statement of fact.

Postulate 1-1

Through any two points there is exactly one line.

Line t is the only line that passes through points A and B.

A B

Postulate 1-2

If two lines intersect, then they intersect in exactly one point.

AE and BD intersect at C. A C B

D E

cPostulates/Axioms

A postulate or axiom is an accepted statement of fact.

Postulate 1-3

If two planes intersect, then they intersect in exactly one line.

Postulate 1-4

Through any three noncollinear points, there is exactly one plane.

Plane RST and Plane STW intersect in ST. R

WS

T

cSketch this…

1. Identify collinear points in the room.

2. Name a plane.

3. Find the intersection of two planes.

4. Draw a plane through three noncollinear points.

cDebrief…

Reread through your notes. On the left side of your math encyclopedia, Google three pictures that will help you process your notes from today. Glue those pictures in your math encyclopedia. Come prepared to report out.

Lesson 1: (1.3) Points, Lines, and Planes

“Dogs have owners. Cats have staff.”

“Dogs feel very strongly that they should always go with you in the car, in case the need should arise for them to bark

violently at nothing right in your ear.”-Dave Barry

HW: Pgs. 19-22; 4-14 evens, 18-24 evens, 38, 40, 46-50 evens, 65-67

Terms: point, space, line, collinear, plane, coplanar, postulate