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Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
flowchart proof
2-column proof
paragraph proof
Vocabulary
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Prove: 2 and 1 are comp.
Use the given flowchart proof to write a two-column proof.
Example 1: Reading a Flowchart Proof
Given: 2 and 3 are comp.1 3
Flowchart proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 1 Continued
Two-column proof:
Statements Reasons
1. 2 and 3 are comp.
1 31. Given
2. m2 + m3 = 90° 2. Def. of comp. s
3. m1 = m3 3. Def. of s
4. m2 + m1 = 90° 4. Subst.
5. 2 and 1 are comp. 5. Def. of comp. s
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 2
Given: RS = UV, ST = TU
Prove: RT TV
Use the given flowchart proof to write a two-column proof.
Flowchart proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 2 Continued
1. RS = UV, ST = TU
2. RS + ST = TU + UV
3. RS + ST = RT, TU + UV = TV
4. RT = TV
5. RT TV
Statements Reasons
1. Given
2. Add. Prop. of =
3. Seg. Add. Post.
4. Subst.
5. Def. of segs.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Prove: 2AB = AC
Use the given two-column proof to write a flowchart proof.
Hw - Example 3
Given: B is the midpoint of AC.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Hw - Example 4
Given: 2 4Prove: m1 m3Two-column Proof:
Use the given two-column proof to write a flowchart proof.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
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.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Use the given paragraph proof to write a two-column proof.
Example 5: Reading a Paragraph Proof
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Paragraph Proof: It is given thatm1 + m2 = m4. 3 and 4 aresupplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 5 Continued
Two-column proof:
Statements Reasons
1. m1 + m2 = m4 1. Given
2. 3 and 4 are supp. 2. Linear Pair Theorem
3. m3 + m4 = 180° 3. Def. of supp. s
4. m3 + m1 + m2 = 180°
4. Substitution
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Hw - Example 6
Given: WXY is a right angle. 1 3Prove: 1 and 2 are complementary.
Use the given paragraph proof to write a two-column proof.
Paragraph Proof: Since WXY is a right angle, mWXY = 90° by the definition of a right angle. By the Angle Addition Postulate, mWXY = m2 + m3. By substitution, m2 + m3 = 90°. Since 1 3, m1 = m3 by the definition of congruent angles. Using substitution, m2 + m1 = 90°. Thus by the definition of complementary angles, 1 and 2 are complementary.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Prove: 3 and 4 are complementary
Example 7: Writing a Paragraph Proof
Given: 1 and 2 are complementary
Use the given two-column proof to write a paragraph proof.
m3 + m4 = 90°
3 and 4 are comp.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 7 Continued
Paragraph proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Hw- Example 8
Given: 1 4Prove: 2 3Two-column proof:
Use the given two-column proof to write a paragraph proof.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Hw - Lesson Quiz
Use the para proof to write a flowchart and 2-column proof.
a paragraph proof