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.

POINTDefinition: 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

LINEDefinition: 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 POINTSDefinition: 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

A C

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.

VerticalHorizontal Plane Plane

B CA

P

PLANENames:

N

D

BA

C

COPLANARDefinition: 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

INTERSECTIONIntersection: 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 1-1Through 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 1-2If 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 1-3If two planes intersect, then they intersect in exactly one line.

Plane RST and plane STW intersect in ST

W

R

TS

POSTULATE 1-4Through any three noncollinear points there is exactly one plane

a) Name the plane on the bottom of the boxb) 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 DABDC

C. Planes EHD and FGCNone

d. Plane EFB andPoint B

e. Plane HEB andPoint C

f. Plane HEF and Point F

HOMEWORKPractice 1-2

Quiz Wednesday!