1. Flowchart and Paragraph Proofs
2-7
Flowchart and Paragraph Proofs
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry

2. Warm Up Complete each sentence.
1. If the measures of two angles are ? , then the angles are congruent.
2. If two angles form a ? , then they are supplementary.
3. If two angles are complementary to the same angle, then the two angles are ? .
equal
linear pair
congruent

3. Objectives
Write flowchart and paragraph proofs.
Converse Postulates

4. Vocabulary
flowchart proof
paragraph proof

5. Note 37
A second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof.
The justification for each step is written below the box.

6. Example 1: Reading a Flowchart Proof
Given: 2 and 3 are comp.
1  3
Prove: 2 and 1 are comp.
Flowchart proof:

7. Note 37 (cont.)
A paragraph proof is a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.

8. Example 3: Reading a Paragraph Proof
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Paragraph Proof: It is given that
m1 + m2 = m4. 3 and 4 are
supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°.

9. Note 38

10. Example 1B: Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30

12. Example 2A: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
4  8
4  8 4 and 8 are alternate exterior angles.
r || s Conv. Of Alt. Ext. s Thm.

13. Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5

14. Check It Out! Example 2b
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
m3 = 2x, m7 = (x + 50), x = 50

15. Lesson Quiz: Part I
Name the postulate or theorem
that proves p || r.
1. 4  5
Conv. of Alt. Int. s Thm.
2. 2  7
Conv. of Alt. Ext. s Thm.
3. 3  7
Conv. of Corr. s Post.
4. 3 and 5 are supplementary.
Conv. of Same-Side Int. s Thm.