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Name: _________________________
Date: _______________
Core-Geo: 2.1 Inductive Reasoning
Warm-up:
1. Solve for x: 8 – 3x = -7
2. Simplify: 8x2 – 8x + 3 – x – 10 + 15x2 + 3x3
3. Simplify: 3(x + y2) + 5(y2 – 5x) + x
1.5 Review
1. Draw a pair of complementary angles.
2. Draw two angles that form a linear pair.
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2.1 Use Inductive Reasoning
Vocabulary
Conjecture
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Inductive Reasoning
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Counterexample
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Example 1: Describe a visual pattern
(a) Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure.
Each rectangle is divided into _______ as many equal regions as the figure number.
Sketch the fourth figure by dividing the rectangle into __________. Shade the section
just ________ the horizontal segment at the _______.
(b) Sketch the fifth figure in the pattern.
Three dots (…) tell you that
the pattern continues.
Example 2: Describe the number pattern
(a) Describe the pattern in the numbers –1, –4, –16, –64, ….
Notice that each number in the pattern is ________ times the previous number.
–1,
–4,
–16,
–64, …
× ___
× ___
× ___
× ___
(b) Write the next three numbers in the pattern.
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Example 3: Make a conjecture
Given five noncollinear points, make a conjecture about the number of ways to connect
different pairs of the points.
Make a table and look for a pattern. Notice the pattern in how the number of connections
___________. You can use the pattern to make a conjecture.
1
2
3
4
____
____
____
____
Number of points
5
•
Picture
Number of
connections
+___
+___
+___
____
+____
Conjecture You can connect five noncollinear points _____ different ways.
Example 4: Find a counterexample
A student makes the following conjecture about the difference of two numbers. Find a
counterexample to disprove the student’s conjecture.
Conjecture
The difference of any two numbers is always smaller than the larger number.
To find a counterexample, you need to find a difference that is ____________ than the
____________ number.
_____– _____ = _____
Because_____
_____, a counterexample exists. The conjecture is false.
Hmwk #7
p. 75 # 3, 5, 7, 11, 13, 30, 40
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