Math 2 Chapter 2 Study Guide
Show all work on separate piece of paper.
Name:________________________
Period:____
1) Determine whether inductive or deductive reasoning is being used. Determine the validity?
a) All swans are white. Mark has a pet swan.
b) Even numbers are divisible by 2. Eight is a
Therefore it must be white.
even number so it must be divisible by 2.
c) Alex is tall, Amy is tall, and Adam is tall. So if
your name starts with ‘A’ you must be tall.
d) Since 3 is prime, 5 is a prime, & 11 is prime.
All primes must be odd.
2) Write each statement as a propositional statement (If-Then Form).
a ) When I get a day off I am going to movies.
b) Junk food makes my stomach hurt.
c ) parallel line have the same slope.
d) The sum of two even numbers is even.
e ) Triangles have three sides.
e) The sum of two even numbers is even.
3) Identify the hypothesis (p) and conclusion (q) of each conditional statement.
a ) If an angle is acute, then its measure is
less than 90 degrees.
p:
q:
What is the truth value of the statement?
b) If it is summer time, then it is sunny.
p:
q:
What is the truth value of the statement?
4) Give a counter example for the following conditional statement.
a) If an animal has spots, then it is a cheetah
b) If an animal has stripes, then it is a tiger.
5) Determine which property is being demonstrated
a)
b)
∠𝐹 ≅ ∠𝐹
a)
𝐼𝑓 𝑎 = 𝑏, then 𝑎 + 7 = 𝑏 + 7
b)
̅̅̅̅,
𝐼𝑓 ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅̅
𝑀𝑁 & ̅̅̅̅̅
𝑀𝑁 ≅ 𝑋𝑌
̅̅̅̅
then ̅̅̅̅
𝐴𝐵 ≅ 𝑋𝑌
𝐼𝑓 𝑋 = 𝑌 , 𝑡ℎ𝑒𝑛 𝑌 = 𝑋
6) Write the converse of the following statement. Then determine the truth value.
a) If a figure is a triangle, then it has three sides.
b) If I am tired, then I should sleep.
c) If lines are parallel then they have the same slope.
d) If a number is even, then it’s divisible by 2.
7) Given the angle use a protractor to draw
& label a non- adjacent supplementary angle.
8) Given the angle use a protractor to draw
& label an adjacent complimentary angle.
𝟏𝟏𝟎°
𝟒𝟎°
𝟐𝟓°
𝟔𝟓°
9) Solve each of the following for x & y. Then identify the property being used.
a)
b)
( 𝒙 − 𝟏𝟎)°
𝟔𝟎°
c)
(𝟏𝟎𝟖)°
y⁰
𝒚⁰
𝟐𝒙°
(𝟓𝒙 − 𝟖)°
𝒙°
10) Given the picture identify the angle that is a…
a)
b)
c)
d)
e)
f)
Complementary Angle to ∠D
Vertical Angle to ∠E
Linear Pair with ∠B
Supplementary Angle to ∠E
Adjacent to ∠B
Congruent to ∠E + ∠D
m
A
E
B
C
D
p
11) Solve for x and then plug in to find the missing measures.
a)
5
2x
x
b)
𝟖𝟎°
35 cm
12) Finish the proof
Given:
𝟑(𝒙 + 𝟕) + 𝒂 = 𝟏𝟖 & 𝒂 = −𝟏𝟐
Prove:
𝑥=3
𝟑(𝒙 + 𝟕) + 𝒂 = 𝟏𝟖 & 𝒂 = −𝟏𝟐
Given
𝟑𝒙°
13) Finish the proof
14) Find the measure of each missing angle. An Explain how you know.
𝑚∠𝑎 = ______________
𝟏𝟐𝟏°
𝑚∠𝑏 = ______________
𝑚∠𝑐 = ______________
c
d
𝑚∠𝑑 = ______________
𝑚∠𝑒 = ______________
b
e
a
Review Problems
15) Find the distance between the points
a) (7,5) & (2,4)
b) (-2,5) & (8,7)
16) Find the Mid-Point between the points
a) (7,5) & (2,4)
17) Solve for x
18) Graph the following Equation
11 − 2(4 + 𝑥) = 23
a) 𝑦 = 𝑥 − 4
2
5
b) 𝑦 = −3𝑥
b) (-2,5) & (8,7)
19) Evaluate
a)
3
5
−
9
2