Chapter 2 Review

1
Chapter 2 Review

• Reasoning and Proof

2
VocabState whether each sentence is true or
false. If false, replace the incorrect word to
make it true.

1. Theorems are accepted as true.
2. In a two-column proof, the properties that
   justify each step are called reasons.
3. The Reflexive Property of Equality states that
   for any number a, aa.
4. The contrapositive of a conditional is formed by
   switching the hypothesis and conclusion of the
   original statement.

3
Inductive Reasoning and Conjecture Make a
conjecture based on the given information. Draw a
figure if necessary.

1. and are supplementary
2. X, Y and Z are collinear and XY YZ

4
Conditional Statements a)Write each statement in
if-then form, then identify the hypothesis and
conclusion. b)Write the converse of the
statement. If it is false give a counterexample.

1. March has 31 days.
2. The intersection of two planes is a line.

5
PostulatesDetermine if each statement is always,
sometimes, or never true. Explain.(use a
postulate or theorem to explain when possible)

1. The intersection of two different lines is a
   line.
2. If P is the midpoint of XY, then XPPY.
3. Four points determine exactly one plane.
4. If MX MY, then M is the midpoint of XY.

6
Algebraic Properties and Proof State the
property that justifies each statement.

1. If 3(x 2)6, then 3x6 6
2. If 10x 20, then x 2
3. If AB 20 45, then AB 25
4. If 3 CD, and CDXY, then 3 XY

7
Algebraic Proof Write a two-column proof.

• If AC AB, AC 4x1 and AB 6x-13, then x 7.

8
Proving Segment Relationship Write a two-column
proof

• Given ABCD
• Prove AC BD

A
B
C
D
9
Angle Relationship Find the measure of the
numbered angle

1. Angle 1
2. Angle 2
3. Angle 3

A
D
F
2
3
73
1
C
B
E
10
Proving Angle Relationships Write a two-column
proof
F

• Given
• Prove

C
E
A
B
11
ANSWERS

• Slide 1
• 1. Postulates are accepted as true.
• 2. True
• 3. True
• 4. The converse of a conditional is formed by
  switching the hypothesis and conclusion of the
  original statement.

12
ANSWERS

• Slide 2
• 1. Angles A and B are a linear pair.
• 2. Y is the midpoint of XZ.

13
ANSWERS

• Slide 3
• 1. a) If it is March, then the month has 31 days.
• - hyp- It is March concl.- the month has 31
  days
• b) If the month has 31 days, then it is March.
• -false There are 31 days in the month of July
• a) If two planes intersect, then the intersection
  is a line.
• -hyp- two planes intersect concl.- it is a line
• b) If the intersection is a line, then two planes
  intersected.
• -true

14
ANSWERS

• Slide 4
• 1. Never, because the intersection of two lines
  is exactly one point.
• 2. Always, that is the definition of a midpoint.
• 3. Sometimes, because 3 points determine exactly
  one plane, the fourth point could be on a second
  plane.
• 4. Sometimes, X and Y could be collinear so the
  lines with X and Y would be intersecting at M and
  therefore M would not be a midpoint.

15
ANSWERS

• Slide 5
• 1. Distributive Property
• 2. Division Property
• 3. Subtraction Property
• 4. Transitive Property

16
ANSWERS

• Given AC AB, AC 4x 1, AB 6x 13
• Prove x 7
• AC AB, AC 4x 1, 1. Given
• AB 6x 13
• 4x 1 6x 13 2. Substitution Prop
• 4x 1 4x 6x 13 4x 3. Subtraction Prop
• 1 2x 13 4. Substitution Prop
• 1 13 2x 13 13 5. Addition Prop
• 14 2x 6. Substitution Prop
• 14/2 2x/2 7. Division Prop
• 7 x 8. Substitution Prop
• x 7 9. Symmetric Prop

17
ANSWERS

• Slide 7
• AB CD 1. Given
• AB BC AC 2. Segment Addition Postulate
• BC CD BD
• CD BC AC 3. Substitution Prop
• AC BD 4. Substitution Prop

Given AB CD Prove AC BD
A
B
C
D
18
ANSWERS

• Slide 8
• 1. angle 1 73 90 angle 1 17
• 2. perpendicular lines rt angles angle2 90
• 3. angles 2 and 3 are vertical angles. Vertical
  angles are congruent. angle 3 90

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ANSWERS
C
F
E
Given Prove
A
B

• ABF is congruent to EBC 1. Given
• ABF EBC 2. Definition of congruent angles
• 3. ABE EBF ABF 3. Angle Addition
  Postulate
• EBF FBC EBC
• 4. ABE EBF EBF FBC 4. Substitution Prop
• 5. ABE EBF EBF 5. Subtraction Prop
• EBF FBC - EBF
• 6. ABE FBC 6. Substitution Prop

Angle symbols should be used in front of each
set of 3 letters