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Transcript 
2-7 Flowchart and Paragraph Proofs
Warm Up
Complete each sentence.
1. If the measures of two angles are
? , then the
two angles are congruent. equal
2. If two angles form a
? , then they are
supplementary. linear pair
3. If two angles are complementary to the same
angle, then the two angles are
Holt McDougal Geometry
? . congruent
2-7 Flowchart and Paragraph Proofs
Learning Targets
I will prove geometric theorems by
using deductive reasoning.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Use the given information to write a twocolumn proof.
Given: 2 and 3 are complementary
1  3
Prove: 2 and 1 are complementary
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example 1 Continued
Two-column proof:
Statements
Reasons
1. 2 and 3 are complementary 1. Given
1  3
2. m2 + m3 = 90°
2. Def. complementary angles
3. m1 = m3
3. Def. congruent angles
4. m2 + m1 = 90°
4. Substitution property
5. 2 and 1 are complementary 5. Def. complementary angles
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Use the given information to write a two-column
proof.
Given: 2  4
Prove: m1  m3
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example Continued
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Use the given paragraph proof to write a twocolumn 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°.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example Continued
Two-column proof:
Statements
1. m1 + m2 = m4
Reasons
1. Given
2. 3 and 4 are supplementary 2. Linear Pair Theorem
3. m3 + m4 = 180°
3. Def. supplementary angles
4. m3 + m1 + m2 = 180° 4. Substitution Property
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Use the given information to write a twocolumn proof.
Given: WXY is a right angle. 1  3
Prove: 1 and 2 are complementary.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example Continued
Statements
Reasons
1. WXY is a right angle. 1  3
1. Given
2. mWXY = 90°
2. Def. right angle
3. m2 + m3 = mWXY
3. Angle addition postulate
4. m2 + m3 = 90°
4. Substitution property
5. m1 = m3
5. Def. congruent angles
6. m2 + m1 = 90°
6. Substitution property
7. 1 and 2 are comp.
7. Def. complementary angles
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Provide the reasons for the two-column proof
shown below.
Given: 1 and 2 are complementary
Prove: 3 and 4 are complementary
m3 + m4 = 90°
3 and 4 are comp.
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example
Use the information to write a two-column
proof.
Given: 1  4
Prove: 2  3
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Example Continued
Holt McDougal Geometry
2-7 Flowchart and Paragraph Proofs
Homework
Page 124, #9 – 16.
Holt McDougal Geometry
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