The document discusses different proof formats: 1) Two-column proof shows the statement in one column and the reasoning in another. 2) Paragraph proof writes out the logic in paragraph form rather than two columns. 3) Flow proof diagrams the logical connections between statements using arrows to show the flow of reasoning.

1. Sections 3.2 and 3.3

2. Two-Column Proof
Paragraph Proof
Flow Proof

3.  What you have seen so far. One column
shows the statement and the other how you
arrived at it.
Statement Reason
1. AB = CD 1. Given
2. AB + BC = BC + CD 2. Addition Property
3. AC = AB + BC 3. Segment Addition Postulate
4. BD = BC + CD 4. Segment Addition Postulate
5. AC = BD 5. Substitution

4.  The argument is made in a normally written
paragraph. Not normally used in math, but a
great form for essays.
 Given that the length of AB equals that of CD,
we know that AB + BC equals BC +CD by the
addition property. By the segment addition
property we see that AC = AB + BC and that
BD = BC + BD. Therefore, using the
substitution property, AC = BD.

5.  Is great for showing logical connections.
AB = CD AB + BC = BC + CD
Given Addition Property
AB + BC = AC AC = BD
Segment Addition
Substitution Prop.
BC + CD = BD
Segment Addition

7.  If two parallel lines are crossed by a
transversal, then their corresponding angle
pairs are congruent
1
Angles 1 and 2 are congruent
2

8.  If two parallel lines are crossed by a
transversal, then the following angle
pairs are congruent:
◦ Alternate Interior Angles
◦ Alternate Exterior Angles.
 Remember also that
Vertical Angles are always congruent.

9.  If two parallel lines are crossed by
a transversal, then the following
angle pairs are supplements:
◦ Consecutive Interior Angles
◦ Consecutive Exterior Angles
 Remember also that
Linear Pairs are always supplements.