Download Lessons 2-1 to 2-3 Review - Rochester Community Schools

Geometry Lessons 2-1 to 2-3 Review
Name __________________________________
LESSON 2.1
In 1-4, Sketch the next figure in the pattern.
1.)
2.)
3.)
4.)
In 5-9, a.) Describe a pattern in the numbers.
b.) Write the next number in the pattern.
c.) Graph the pattern on a number line.
6.)
1 3 5 7
, , , ...
3 4 35 36
4
3
5.) 113, 224, 335, 446,...
7.) 3, 0, –3, –6,…
8.) 1, 4, 9, 16,…
9.) 2, 3, 5, 7, 11…
In 10-13, Show the conjecture is false by finding a counterexample.
10.) The quotient of two whole numbers is a whole number.
11.) If m  –1, then
m
< 1.
m 1
12.) The Square root of a number x is always less than x
In 13-16, Write a function rule relating x and y.
13.) x
1
2
3
y
1
8
27
14.) x
y
1
2
–5 –3
3
–1
15.) x
1
2
3
y
4
3
2
16.) x 1
y
1
2
4
0. 5
0.25
17.) Suppose you are studying bacteria in biology class. The table shows the number of bacteria after n
doubling periods. Your teacher asks you to predict the number of bacteria after 7 doubling periods. What
would your prediction be? n (periods)
0 1 2 3
4
5
billions of bacteria
4
8
16 32
64
128
LESSON 2.2
In 18-21, Rewrite the conditional statement in if-then form.
18.) It is time for dinner if it is 6 P.M.
19.) There are 12 eggs if the carton is full.
20.) An obtuse angle is an angle that measures
more than 90° and less than 180°.
21.) The car runs when there is gas in the tank.
In 22 and 23, Write the Converse, Inverse, and Contrapositive of each statement.
22.) If you like hockey, then you will go to the hockey game.
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23.) If x is odd, then 3x is odd.
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In 24-27, Decide whether the statement is true or false. If false, provide a counterexample.
24.) The equation 4x – 3 = 12 + 2x has exactly one solution.
25.) If x2 = 36, then x must equal 18 or –18.
26.) If mA  122°, then the measure of the supplement of A is 58°.
27.) Two lines intersect in at most one point.
In 28 and 29, Write the converse of each true statement. If the converse is also true, combine the
statements to write a true biconditional statement.
28.) If two angles are supplementary, then their sum is 180°.
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29.) If an animal is a panther, then it lives in the forest.
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In 30 and 31, Rewrite the biconditional statement as a conditional statement and its converse.
30.) Two lines are perpendicular if and only if they intersect to form right angles.
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31.) A point is a midpoint of a segment if and only if it divides the segment into two congruent segments.
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In 32 and 33, Decide whether the statement is a valid definition.
32.) If a number is divisible by 2 and 3, then it is divisible by 6.
33.) If two angles are not adjacent, then they are vertical angles.
LESSON 2.3
In 34-37, Determine if statement (3) follows from statements (1) and (2) by either the Law of Detachment
or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.
34.) (1)If an angle measures more than 90°, then it is not acute.
(2) mABC = 120°
(3)ABC is not acute.
35.) (1) All 45° angles are congruent.
(2) A  B
(3)A and B are 45° angles.
36.) (1) If you wear the school colors, then you have school spirit.
(2) If you have school spirit, then the team feels great.
(3) If you wear the school colors, then the team will feel great.
37.) (1) If 2 is acute, then 3 is obtuse.
(2) If 3 is obtuse, then 4 is acute.
(3) If 2 is acute, then 4 is acute.
In 38 and 39, Decide whether inductive or deductive reasoning is used to reach the conclusion. Explain
your reasoning.
38.) For the past three Wednesdays, the cafeteria has served macaroni and cheese for lunch. Dana concludes
that the cafeteria will serve macaroni and cheese for lunch this Wednesday.
39.) If you live in Nevada and are between the ages of 16 and 18, then you must take driver’s education to get
your license. Anthony lives in Nevada, is 16 years old, and has his driver’s license. Therefore, Anthony
took driver’s education.
In 40-43, Use the true statements below to determine whether you know the conclusion is true or false.
Explain your reasoning.
If Dan goes shopping, then he will buy a pretzel.
If the mall is open, then Jodi and Dan will go shopping.
If Jodi goes shopping, then she will buy a pizza.
The mall is open.
40.) Dan bought a pizza.
41.) Jodi and Dan went shopping.
42.) Jodi bought a pizza.
43.) Jodi had some of Dan’s pretzel.