Section 1.2
Section 1.2
Section 1.2
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<strong>1.2</strong><br />
Exercises<br />
Guided Practice<br />
Vocabulary Check<br />
1. Explain what a conjecture is.<br />
2. How can you prove that a conjecture is false?<br />
Skill Check<br />
Complete the conjecture with odd or even.<br />
3. Conjecture: The difference of any two odd numbers is __?__.<br />
4. Conjecture: The sum of an odd number and an even number<br />
is __?__.<br />
Show the conjecture is false by finding a counterexample.<br />
5. Any number divisible by 2 is divisible by 4.<br />
6. The difference of two numbers is less than the greater number.<br />
7. A circle can always be drawn around a four-sided shape so that it<br />
touches all four corners of the shape.<br />
Practice and Applications<br />
Extra Practice<br />
See p. 675.<br />
8. Rectangular Numbers The dot patterns form rectangles with a<br />
length that is one more than the width. Draw the next two figures<br />
to find the next two “rectangular” numbers.<br />
2<br />
6<br />
12<br />
20<br />
9. Triangular Numbers The dot patterns form triangles. Draw the<br />
next two figures to find the next two “triangular” numbers.<br />
1<br />
3<br />
6<br />
10<br />
Homework Help<br />
Example 1: Exs. 8−16<br />
Example 2: Exs. 8−16<br />
Example 3: Exs. 17–19<br />
Example 4: Exs. 17–19<br />
Technology Use a calculator to explore the pattern. Write a<br />
conjecture based on what you observe.<br />
10. 101 25 __?__ 11. 11 11 __?__ 12. 3 4 __?__<br />
101 34 __?__ 111 111 __?__ 33 34 __?__<br />
101 49 __?__ 1111 1111 __?__ 333 334 __?__<br />
<strong>1.2</strong> Inductive Reasoning 11
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