WARM-UP 2/1/13

Describe any points, lines and planes you see in this picture

UNIT 2: INTRODUCTION TO GEOMETRY

Essential Question:

How do the basic properties of geometry apply to the real world? How do you use deductive reasoning, logic, and mathematical properties to help you draw conclusions?

Bonus Question:

Write real-world examples of conditionals and converses that meet the following criteria, and explain each answer.

A) Write a conditional that is true but whose converse is false.

B) Write a true conditional whose converse is also true.

POINT

Definition: A point is an indication of a location. A point has no size.

A point is represented by a small dot and is named by a capital letter

Example: Name: Point AA

Points, Lines, and Planes

LINE

Definition: A line is a series of points that extends in two opposite directions without end.

You can name a line by any two points on the line. Another way to name a line is with a single lowercase letter.

Names:

**must be only two points**

m

AB

C

COLLINEAR POINTS

Definition: Collinear points are points that lie on the same line.

In the picture below, points A and B are collinear but C is not

Name the collinear points:

B

AC

PLANEDefinition: A plane is a flat surface that has no thickness. A plane contains many lines and extends without end in the directions of all its lines.

You can name a plane by either a single capital letter or by at least three of its non-collinear points.

Vertical

Horizontal Plane Plane

B CA

P

PLANE

Names:

N

D

BA

C

COPLANAR

Definition: Points and lines in the same plane are coplanar.

N

D

BA

C

P

M

NAMING A PLANE

SPACE:

Space is the boundless, three-dimensional set of all points

INTERSECTION

Intersection: the set of points that two figures have in common.

BASIC POSTULATES OF GEOMETRY

(A Postulate is a rule accepted as true without proof)

Draw two points and connect the points.

What is the geometric figure.

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.

B

A

t

POSTULATE 1-2

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

AE and BD intersect at C

B

D E

A

C

What is the intersection of the front wall and the ceiling?

POSTULATE 1-3

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

Plane RST and plane STW intersect in ST

W

R

TS

POSTULATE 1-4

Through any three noncollinear points there is exactly one plane

a) Name the plane on the bottom of the box

b) Shade the plane that contains E, H, and C.

c) Name another point that is in the same plane of point A, B, and C.

d) Name another point that is coplanar with points E, H, and C.

e) Are points A and G collinear?

2. NAME THE INTERSECTION OF…

A. Planes HGF and GCB

GF

B. Planes HDC and DAB

DC

C. Planes EHD and FGC

None

d. Plane EFB and

Point B

e. Plane HEB and

Point C

f. Plane HEF and

Point F

LINE SEGMENT

Definition: A segment is a part of a line consisting of two endpoints and all points between

Names: or

Line Segments, Rays, Parallel Lines and Planes

RAY

Definition: A ray is the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.

OPPOSITE RAYS

Name three segments.

Name four different rays.

Name two opposite rays.

Perpendicular Lines: lines that intersect to form right angles.

M

n

WHAT ARE PARALLEL LINES?

Are you sure you have the correct definition?

Definition: Parallel Lines are coplanar lines that do not intersect

What other type of lines do not intersect????

SKEW LINES

Definition: Skew Lines are noncoplanar lines that do not intersect

Are there any in the classroom?

Name the segments parallel to: AB

EH

DC

Name a pair of skew lines.

PARALLEL PLANES:

Parallel Planes: planes that do not intersect.

EX. Top ll bottom

HGFE ll DCBA

NAME A PAIR OF PARALLEL PLANES.

HOMEWORK

1-3 Segments, Rays, Parallel Lines and Planes Worksheet

Quiz Wednesday!