Section 1.3: Points, Lines, and PlanesGoal: Be able to understand basic terms and postulates of geometry.

Warm up: Solve the system of equations.

y = 2x – 4

4x – y = 10

4x – (2x – 4) = 10 2x + 4 = 10 2x = 6 x = 3

(3, 2)

y = 2(3) – 4y = 2

(3, 2)

-2x + y = - 4 4x – y = 10

2x = 6 x = 3

y = 2(3) – 4y = 2

(3, 2)

Graphing Substitution Elimination

point - ______________________ ______________________

Location with no size, represented by a

small dot, named by a capital letter

A

______________________________

______________________________

a geometric figure consist of

a set of points

space - ______________________a boundless, 3-D set of all points

line - ________________________ ________________________

series of points that extends in

two opposite directions without end

P

Q m

PQ

QP

line PQ

line m

Points that lie in the same line are

_______________. collinear points (PQ are collinear)

In the figure below, name 3 points that are collinear and 3 points that are not collinear

X

Y Z W

Y, Z, and W are collinearX, Y, and Z are not collinearX, W, and Z are not collinear

(noncollinear).

Why are arrowheads on the lines?

Plot __________________________________

__________________________________

A(0, -4), B (2, 2), and C(3, 5) on a coordinate

plane.

A

B

C

_____________________________________________

_____________________________________________

What are your observations? Points A, B, and C are

collinear.

plane - _______________________ _______________________ _______________________ _______________________

a flat surface that has no thickness;

contains many lines

infinitely far in the direction of itslines.

R

A

B

C

Plane R Plane ABC *A, B, C are

noncollinear points

Points and lines in the same plane are ___________. coplanar

and extends

1. Name two different planes that contain points C and G.

A

B

C

D

E

H

G

F

J

2. Name the intersection of plane AED and plane HEG.

3. How many planes contain the points A, F, and H?

plane BCG, plane DCG

HE

(3 noncollinear points) 1

postulate - _____________________ _____________________

or axiom; an accepted

statement of fact

Postulate 1-1_________________________

______________________________

Through any two points,there

is exactly one line.

A

B m

Postulate 1-2 ________________________

______________________________

If two lines intersect,

intersect in exactly one point.

Postulate 1-3 ________________________

______________________________intersect in exactly one line.

P

QR

S

Plane PQR and Plane QRS intersect at QR

then they

If two planes intersect,

then they

Postulate 1-4 ___________________________

______________________________

Through any 3 noncollinear points

there is exactly one plane.

A

B

C

Plane ABC

What is the difference between a postulate and a

conjecture?