warm - up. section 1.1 inductive reasoning geometry
TRANSCRIPT
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WARM - UP
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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
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OBJECTIVES
• Learn how to use inductive reasoning to make conjectures
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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.
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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!
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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.
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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
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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
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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
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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.
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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
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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
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TWO DIMENSIONS
• Plane A plane extends in two dimensions.
• It is usually represented by a shape that looks like a tabletop or wall.
A
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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.
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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
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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
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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
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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