Name
Class
Date
Practice 4-5
Example Exercises
Example 1
Use indirect reasoning to prove each statement.
1. If Andre spends more than $35 to buy two items at a sporting goods
store, then at least one of the items costs more than $17.50.
2. If LaShonda spends more than $15 to buy three books at a local book
store, then at least one of the books costs more than $5.
3. If 17 students are assigned to 16 lockers, then at least one locker has
more than one student assigned to it.
4. If Grace jogs more than 4 mi in total on Saturday and Sunday, then she
jogs more than 2 mi on at least one of those days.
5. If Joel sells three candy bars for more than $1.50, then at least one of the
candy bars costs more than $.50.
Example 2
Write the first step of an indirect proof of each statement.
6. /A > /B
9. It is snowing outside.
7. nDEF is equilateral.
10. ABCD is a square.
8. WX i YZ
11. m/A < 135
Identify the pair of statements that forms a contradiction.
12.
I. m/A 2 m/B 5 0
II. m/B < m/A
III. /A and /B are complementary.
13.
I. ABC is a scalene triangle.
II. m/B > m/A
III. m/A 5 m/C
15. Write an indirect proof that nABC is not a scalene triangle.
A
7
5
B
26
Using Indirect Reasoning
© Prentice-Hall, Inc.
14. Mr. Ramirez always eats pizza for lunch on Tuesday. Today he is eating a
taco for lunch. What conclusion follows from the pair of statements?
7
C
Geometry Chapter 4