Sections 3.2 and 3.3

Two-Column Proof

Paragraph Proof

Flow Proof

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

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.

Is great for showing logical connections.

AB = CD

AB + BC = AC

AB + BC = BC + CD

BC + CD = BD

AC = BD

Given Addition Property

Segment Addition

Segment Addition

Substitution Prop.

If two parallel lines are crossed by a transversal, then their corresponding angle pairs are congruent

1

2

Angles 1 and 2 are congruent

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.

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.