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Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs2-7 Ways to write Proofs
Holt Geometry
Quiz on Monday
Holt McDougal Geometry
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
flowchart proof
2-column proof
paragraph proof
3 ways to write Proofs
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Prove: 2AB = AC
Example 1: Writing a Flowchart Proof
Given: B is the midpoint of AC.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 1
Flowchart proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 2
Given: 2 4Prove: m1 m3
write a flowchart proof.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 3
Given: WXY is a right angle. 1 3Prove: 1 and 2 are complementary.
Write a Flowchart proof.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Check It Out! Example 3 Continued
Statements Reasons
1. WXY is a right angle. 1. Given
2. mWXY = 90° 2. Def. of right angle
3. m2 + m3 = mWXY 3. Angle Add. Postulate
4. m2 + m3 = 90° 4. Subst.
5. 1 3 5. Given
6. m1 = m3 6. Def. of s
7. m2 + m1 = 90° 7. Subst.
8. 1 and 2 are comp. 8. Def. of comp. angles
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Prove: 3 and 4 are complementary
Example 4: 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 4 Continued
Paragraph proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 5
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
It is given that 1 4. By the Vertical Angles Theorem, 1 2 and 3 4. By the Transitive Property of Congruence, 2 4. Also by the Transitive Property of Congruence, 2 3.
Check It Out! Example 5 Continued
Paragraph proof:
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Lesson Quiz
Use the two-column proof at right to write the following.
1. a flowchart proof
2. a paragraph proof