1. Warm Up Complete 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

2. Learning Targets
I will prove geometric theorems by using deductive reasoning.

4. Example Given: 2 and 3 are complementary 1  3
Use the given information to write a two-column proof.
Given: 2 and 3 are complementary
1  3
Prove: 2 and 1 are complementary

5. Statements Reasons Example 1 Continued Two-column proof: 1  3
1. 2 and 3 are complementary
1  3
1. Given
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

6. Example Use the given information to write a two-column proof.
Prove: m1  m3

7. Example Continued

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

9. Statements Reasons Example Continued Two-column proof:
1. m1 + m2 = m4
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

10. Example Use the given information to write a two-column proof.
Given: WXY is a right angle. 1  3
Prove: 1 and 2 are complementary.

11. 1. WXY is a right angle. 1  3 1. Given 2. mWXY = 90°
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

12. 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.

13. Example Use the information to write a two-column proof.
Given: 1  4
Prove: 2  3

14. Example Continued

15. Homework
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