Page 169 - Math Course 2 (Book 2)

Inductive Reasoning and Conjecture

Real World Example Geometric Conjecture

UNEMPLOYMENT Given: ACE is a right triangle with AC = CE. Which

Based on the table showing unemployment rates figure would illustrate the following conjecture?
for various counties in Texas, find a counterexam- ΔACE is isosceles, ∠C is a right angle, and AE is the
ple for the following statement.
hypotenuse.
The unemployment rate is highest in the cities
with the most people. A. B.

Country Population Rate

Armstrong 2,163 3.7%

Cameron 371,825 7.2%

El Paso 713,126 7.0% C. D.

Hopkins 33,201 4.3%

Maverick 50,436 11.3%

Mitchell 9,402 6.1%

Examine the data in the table. Find two cities such Answer
that the population of the first is greater than the
population of the second while the unemployment
rate of the first is less than the unemployment rate Real World Example
of the second.
Licensed Drivers
El Paso has a greater population than Maverick Based on the table showing licensed drivers in
while El Paso has a lower unemployment rate than various states, find a counterexample for the
Maverick. following statement.

Maverick has a population of The licensed driver rate is lowest in the states with
50,436 people in its popula- the most people.
tion, and it has a higher rate of
Answer
unemployment than El Paso, State Population Licensed
which has 713,126 people in its Drivers Per 1000
population.
Alabama 4,447,100 792

Your Turn! California 33,871,648 627
Texas 20,851,820 646
Patterns and Conjecture
Vermont 608, 827 831
Make a conjecture about the next number based on
the pattern. West Virginia 1,808,344 745

1
1
1
1
1, , , , Wisconsin 5,363,675 703
4 9 16 25
A. Texas & California
1 1 B. Vermont & Texas
A. 32 B. 36 C. Wisconsin & West Virginia
D. Alabama & West Virginia
1 1
C. D. Answer Answer
34 25

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