Discovering Geometry
Sample Problems from Chapter 1.  Inductive Reasoning.
Mrs. Pat Brewster
These problems may be worked and turned in for Extra Credit homework points.
They are due by the day we take the Chapter 1 Test, but may be turned in earlier.
They will not be accepted later than the day of the test.
Instructions:All problems are to be copied onto your paper.  Work must be shown on all problems and must be neat and organized, to get credit..
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1.  Find the next two terms in the sequence 14, 17, 20, 23, 26, ____, _____, and describe the pattern that helped you find those terms.
Next 2 terms: _____, _____
Explanation:

2.  "The Handshake Problem."
There were 25 people at a party.  Each person shook hands exactly once with everyone else. 
How many handshakes were there?  Use the Handshake Problem formula.

3.  A polygon has 230 diagonals.  How many sides are there in the polygon.
Use the formula for the number of diagonals of a polygon.

4.  Copy and complete this chart.  Be sure to show the factors.

Term:
1
2
3
4
6
20
 n 
Value:
3
16
39
72
?
?
?
Factors:

 

              
Value for 6th term:________
Value for 20th term:________
Value (formula) for nth term:________
5.  Think of a situation you observed outside of school in which inductive reasoning was used correctly.  Write a paragraph or two describing what happened and explaining why you think it was good inductive reasoning.

6.  Draw the next shape in the picture pattern below:

Explain your design of  the 4th pattern.  If you don't have colored pencils, you can just say what the colors should be.

7.  CHALLENGE PROBLEM:  Describe the100th design of the pattern of Problem 6.