Download Study Guide for Test on Chapter 2 (optional)

Chapter 2 Study Guide
Name
1) Find the next number in the pattern: 2, 5, 8, 11, 14, _____________
2) Draw the next picture in the pattern:
_________________
3) Make a conjecture: The product of two even numbers is _____________.
4) Find a counterexample: “Every pair of supplementary angles includes one obtuse angle.”
5) Find a counterexample: “If two rays have the same endpoint, then they are opposite rays.”
(Draw a picture)
Determine if the conclusion was made by inductive or deductive reasoning.
6) Every Sunday my sister watches the Walking Dead, so this Sunday she is going to watch the
Walking Dead. _____________
7) Fingerprints are collected at a crime scene, matched to a suspect and that suspect is arrested
for the crime. ______________
8) Buster uses the Linear Pair Theorem to conclude that every linear pair is supplementary.
____________
Identify the following then decide if a biconditional can be written. If not, write a
counterexample.
9) If m1  120 , then 1 is obtuse.
True/False
Hypothesis: _______________________________________________
Conclusion: _______________________________________________
Converse: ________________________________________________ True/False
Biconditional: ______________________________________________
Counterexample: ___________________________________________
10) If two angles are supplementary, then their sum is 180o.
True/False
Hypothesis: _______________________________________________
Conclusion: _______________________________________________
Converse: ________________________________________________ True/False
Biconditional: ______________________________________________
Counterexample: ___________________________________________
Justify each statement.
11) If 6x + 7 = 29, then 6x = 22
12) If 6x = 36, then x = 6
𝑥
13) If 9 = 2, then x = 18
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
14)
15)
16)
17)
18)
19)
20)
If 3x - 5 = -22, then 3x = -18
If a = x + 3 and a = 2, then 2 = x + 3
3(x + y) = 3x + 3y
If ∠𝐴 ≅ ∠𝐵 and ∠𝐵 ≅ ∠𝐶, then ∠𝐴 ≅ ∠𝐶
If x = 4 + y, then 4 + y = x
AB + BC = AC
If X is the midpoint of ̅̅̅̅
𝐴𝐵 , then AX = XB
⃗⃗⃗⃗⃗ bisects ∠𝐶𝑋𝐵, then 𝑚∠𝐶𝑋𝐸 = 𝑚∠𝐸𝑋𝐵
21) If 𝑋𝐸
22) XE = XE
23) 𝑚∠𝐴𝑋𝐸 + 𝑚∠𝐸𝑋𝐵 = 𝑚∠𝐴𝑋𝐵
21)
22)
23)
Solve each equation and justify each step in a two column proof.
24) -47 = 3x - 59
25) 5( x  3)  4( x  2)
Supply the missing reasons in each proof.
26) Given: ML = ID
Prove: MI = LD
Statements
1. ML = ID
2. MI + IL = ML
LD + IL = ID
3. MI + IL = LD + IL
4. IL = IL
5. MI = LD
●
M
●
I
●
L
●
D
Reasons
1.
2.
3.
4.
5.
27) Given: The picture at the right
Prove: n = 26
1.
2.
3.
4.
5.
6.
Statements
mXYZ  m2  m3
4n – 6 = 58 + (2n – 12)
4n – 6 = 2n + 46
2n – 6 = 46
2n = 52
n = 26
Reasons
1.
2.
3.
4.
5.
6.
28) Given: ABC is a right angle
𝑚∠𝑋𝐵𝐶 = 45𝑜
⃗⃗⃗⃗⃗ bisects ∠𝐴𝐵𝐶
Prove: 𝐵𝑋
1.
2.
3.
4.
5.
6.
7.
8.
9.
Statements
ABC is a right angle.
mABC=90o
mXBC  45
mABX  mXBC  mABC
mABX  45  90
mABX  45
𝑚∠𝐴𝐵𝑋 = 𝑚∠𝑋𝐵𝐶
ABX  XBC
⃗⃗⃗⃗⃗
𝐵𝑋 bisects ABC
Reason Bank
Angle Addition Postulate
Segment Addition Postulate
Reflexive
Symmetric
Transitive
Distributive
Substitution
Addition
Simplify
Reasons
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reason Bank
Subtraction
Multiplication
Division
Definition of Congruent Angles
Definition of Congruent Segments
Definition of Midpoint
Definition of Angle Bisector
Definition of Right Angle