22-7-7Flowchart and Paragraph Proofs Ways to write Proofs

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs2-7 Ways to write Proofs

Holt Geometry

Quiz on Monday



2-7 Flowchart and Paragraph Proofs

flowchart proof

2-column proof

paragraph proof

3 ways to write Proofs



Prove: 2AB = AC

Example 1: Writing a Flowchart Proof

Given: B is the midpoint of AC.



Example 1

Flowchart proof:



Example 2

Given: 2 4Prove: m1 m3

write a flowchart proof.



Example 3

Given: WXY is a right angle. 1 3Prove: 1 and 2 are complementary.

Write a Flowchart proof.



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



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.



Example 4 Continued

Paragraph proof:



Example 5

Given: 1 4Prove: 2 3Two-column proof:

Use the given two-column proof to write a paragraph proof.



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:



Lesson Quiz

Use the two-column proof at right to write the following.

1. a flowchart proof

2. a paragraph proof

22-7-7Flowchart and Paragraph Proofs Ways to write Proofs

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