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S E C T I O N 1 . 1I N D U C T I V E R E A S O N I N G

GEOMETRY

OBJECTIVES

• Learn how to use inductive reasoning to make conjectures

VOCABULARY

• A conjecture is an unproven statement that is based on observations. http://www.youtube.com/watch?v=J9_yarjL3RQ

• A counterexample is an example that shows a conjecture is false.

Example: I might look at your algebra review and make the conjecture that you didn’t know how to solve algebraic equations.

The counterexample would be that your algebra review was good.

TYPES OF REASONING

• Inductive reasoning is a process that includes looking for patterns and making conjectures.

This shows an example of inductive reasoning. You found the pattern and made a conjecture of what the next one should be!

PAPER IN THE MIDDLE ACTIVITY

In groups of 4, tear and make 5 half sheets of paper.On each half sheet of paper add one of these patterns.

• 7, 14, 21, 28, _______, _______, _______, _______• 2, 5, 8, 11, ______, _______, _______, _______• 5, 7, 10, 14, _______, _______, _______, _______• 5, 7, 11, 17, _______, _______, _______, _______• 2, 5, 11, 23, _______, _______, _______, _______

Describe the pattern.

SAGE AND SCRIBE

• Remember this?• Complete the table for the following function and make a

graph• Y=3x – 4

X Y

-3

-2

-1

0

1

S E C T I O N 1 . 2B U I L D I N G B L O C K S O F G E O M E T R Y

GEOMETRY

LESSON OUTCOMES

• Students should be able to give the appropriate notation for line, segment, and ray

• Students should be able to draw representations of given geometric situations

• Students should be able to determine whether points are collinear or coplanar

BASIC PARTS OF GEOMETRIC FIGURES

• Points• Lines• Planes• Segments• Rays• Angles

• Try to find something in the room or in your backpack that you think would represent these things.

ZERO DIMENSION

• Point: • A point has no

dimension. • It is usually

represented by a small dot.

• What does it mean to have no dimension?

• Label a point with a letter A

ONE DIMENSION

• Line: A line extends in one dimension.

B

A

AB

Line Segment: A line segment is part of a line that consists of two points, called endpoints, and all points on the line between the endpoints.

B

A

Ray: A ray is part of a line that consists of a point, called an initial point, and all points on the line that extend in one direction.

AB

B

A

AB

TWO DIMENSIONS

• Plane A plane extends in two dimensions.

• It is usually represented by a shape that looks like a tabletop or wall.

A

BASIC PROPERTIES

• Collinear points Collinear points are points that lie on the same line.

• Coplanar points Coplanar points are points that lie on the same plane.

INTERSECTIONS

• Intersect Two or more geometric figures intersect if they have one or more points in common.

• Intersection The intersection of two or more geometric figures is the set of points that the figures have in common.

AB and CD intersect at point E

E

D

C

B

A

OPPOSITE RAYS

• Opposite rays: • So, opposite rays form a _________?If C is between A and B on AB, then CA

and CB are opposite rays

C BA

ANGLES

• Angle An angle consists of two different rays that have the same initial point.

• Angles are the basic building block for all figures that you know!

C B

A

EXIT TICKET HOMEWORK

1.) Predict the next number in the sequence.

5, 8, 13, 20, 29, ?

True or False

2.) and are collinear?

3.) and are coplanar?

Pg. 6: 12-23Pg. 13: 9-35, 48-51