Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Warm UpComplete each sentence.

1. If the measures of two angles are ? , then the

two 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

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

I will prove geometric theorems by using deductive reasoning.

Learning Targets

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Prove: 2 and 1 are complementary

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

Example

Given: 2 and 3 are complementary1 3

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example 1 Continued

Two-column proof:

Statements Reasons

1. 2 and 3 are complementary

1 31. Given

2. m2 + m3 = 90° 2. Def. complementary angles

3. m1 = m3 3. Def. congruent angles4. m2 + m1 = 90° 4. Substitution property

5. 2 and 1 are complementary 5. Def. complementary angles

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example

Given: 2 4Prove: m1 m3

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

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example Continued

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

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

Example

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 Continued

Two-column proof:

Statements Reasons

1. m1 + m2 = m4 1. Given

2. 3 and 4 are supplementary 2. Linear Pair Theorem

3. m3 + m4 = 180° 3. Def. supplementary angles

4. m3 + m1 + m2 = 180° 4. Substitution Property

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example

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

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

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example Continued

Statements Reasons

1. WXY is a right angle. 1 3 1. Given

2. mWXY = 90° 2. Def. right angle

3. m2 + m3 = mWXY 3. Angle addition postulate

4. m2 + m3 = 90° 4. Substitution property

5. m1 = m3 5. Def. congruent angles

6. m2 + m1 = 90° 6. Substitution property

7. 1 and 2 are comp. 7. Def. complementary angles

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Prove: 3 and 4 are complementary

Example

Given: 1 and 2 are complementary

Provide the reasons for the two-column proof shown below.

m3 + m4 = 90°

3 and 4 are comp.

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example

Given: 1 4 Prove: 2 3

Use the information to write a two-column proof.

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Example Continued

Holt McDougal Geometry

2-7 Flowchart and Paragraph Proofs

Homework

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