1. Introduction to Geometry
NIMS GEO. June 14, 2010
Introduction to Geometry

2. Notecard Information
Name
Grades
Favorite Geometry Shaper

3. What did the acorn Say when he grew up?
Gee, I’m a Tree

4. What is Geometry?
Technical meaning
Your definitions

5. Geometry
Is all about
Constructions
(or Connections)

6. Geometry Start with a small set An initial criteria
See what you can build, construct, connect
Physical and Mental Constructions

7. A simple sheet of paper What do you know? Where can you go?
How can you show?

8. The paper Is what shape? How many lines of symmetry does it have?
How do you know?
How many lines of symmetry does it have?
How do you show?
What other properties does it have?
Where can you go?

9. Paper Fold
Folds 1 2 3 4
Sections

10. Geometry is Connected to Algebra!
Paper Fold
Folds 1 2 3 4
Sections 8 16
This is a Geometric Sequence.
These occur when you multiply by the same rate each time.
In this case, that rate is 2 and the function would be
Y = 1 * 2x
Where X is the number of Folds and Y is the number of sections.
The value 1 represents the initial amount.
Geometry is Connected to Algebra!

11. Paper Fold
Folds 1 2 3 4
Area

12. Geometry is Connected to Algebra!
Paper Fold
Folds 1 2 3 4
Area
1/2
1/4
1/8
1/16
This is a Geometric Sequence.
These occur when you multiply by the same rate each time.
In this case, that rate is (1/2) and the function would be
Y = 1 * (1/2)x
Where X is the number of Folds and Y is the resulting area.
The value
Geometry is Connected to Algebra!

13. 1. This is a _____________Sequence.
Paper Fold Extension Suppose the original area of your paper was 88 square units. If you fold as before, fill in the following table and answer the questions below
Folds 1 2 3 4
Area 88
1. This is a _____________Sequence.
In this case, the rate is (1/2) and the original area is ___________
The function could be written as
Y = ______* (_____)x
Where X is the number of Folds and Y is the resulting area.

14. Paper Fold Bonus
Take any sheet of paper and fold as we did in class (so that each fold is the perpendicular bisector of the previous fold) times
Bring in the folded paper and be able to show me the folds and resulting sections

15. You can learn (construct) a lot from a sheet of paper
You can also learn (constuct) a lot from a notecard
In this case, we are going to let our notecard represent a plane
A plane is a 2 dimensional flat shape with infinite length and width

16. Building Blocks of Geometry
Point
No dimension, infinitely small
Line
1 dimension (length),
Plane
2 dimensions (length and width)
Different geometries define or represent these items differently!
These all reside in Space (3 dimensions)

17. For Euclidean geometry Our notecard represents a plane
Draw 3 noncollinear points on your plane
Draw three lines connecting each pair of points
Label the points A, B and C

18. What do we know?
Point, Line, Plane
Segments
Rays
Angles
Triangles…

19. Where Can we go? Vertical angles are equal
Angles that form a linear pair are supplementary
Other triangle properties tomorrow
Hang on to this ‘plane’ notecard

20. How can we show?
For vertical angles?
Measure
Trace and Place
Fold?

21. What if we started with a circle?
What can we construct?
What do we know?
What can we show?
How do we know?

22. Circle The set of all points in a plane equidistant from a given point
The common distance is called the radius
The given point is called the center
Find the center of your circle…
Where can we go……..

23. June 14 Assignments Due June 15
Complete Paper Fold extension (and bonus if you wish)
Read the Geometry, More than Shapes article
Read pages 5-6 in text and see if you can find a more technical term for a truncated tetrahedron
Use your circle fold to complete questions on page 7 of text—be able to describe (draw or show) 4 polygons with the indicated areas
Complete you definitions tasks
Complete Activity 3.11 on page 127 in your text
(What can you construct or create??)
Goto the NIMS Geo Wiki to download and complete Reflection Journal

24. NIMS websites Mann’s homepage Olsen’s homepage NIMS homepage
Olsen’s homepage
NIMS homepage
NIMS Geometry Wiki
Syllabus and reflection
Daily notes and assignments
Other resources—check regularly