1. Congruent Supplements and Complements
Section 2.4
By: Ellen Wildner

2. Objective or Goal After studying this section you will be able to…
Prove angles congruent by using four new theorems that you will learn in this section

3. Review Complementary Angles
2 angles are complementary if the sum of their measures is
For Ex.
therefore must equal…

4. Review Continued Supplementary Angles
2 angles are supplementary if the sum of their measures is
For Ex.
therefore must equal…

5. Now we begin…Theorem 4
Theorem 4: If angles are supplementary to the same angle, then they are congruent.
For ex. In the diagram to the right is supplementary to , and is also supplementary to
Therefore we can prove that…

6. Sample Problem Thm 4. Given: is supp. to is supp. to Prove: Statements
Reasons
is supp. to
1. Given
is supp. to
2. Given 3.
3.Given 4.
4. If angles are supplementary to angles they are

7. Theorem 5
Theorem 5: If angles are supplementary to congruent angles, then they are congruent.
For ex. It is given that
is supp. to
And that
Therefore we can prove that…

8. Sample Problem Thm. 5 Given: supp. of supp. of Conclusion: Statements
Reasons
supp. of Given
supp. of Given
Given
If 2 angles are supp. To angles they are

9. Theorem 6
Theorem 6: If angles are complementary to the same angle, then they are
For ex. It is given that comp
and comp
Therefore we can prove that…

10. Sample Problem Thm. 6 Given: comp comp Conclusion: Statements Reasons
comp Given
comp Given
If angles are complementary to the same angle, then they are

11. Theorem 7
Theorem 7: If angles are complementary to congruent angles, then they are congruent.
For ex. It is given that comp and comp
Therefore we can prove that…

12. Sample Problem Thm. 7 Given: comp to comp to Conclusion:
Statements Reasons
comp to Given
comp to Given
Given
If angles are complementary to congruent angles, then they are congruent.

13. Practice Problems Given: is comp to is comp to Conclusion:
Statements Reason
is comp to Given
is comp to Given
If angles are complementary to the same angle they are congruent

14. Practice Problems Applying skills Given: is comp to = a. = 49 b. = 131
d = 41
e = 139
= 41
= 139

15. Practice Problems Given: Diagram as shown Prove: Statements Reasons
1. Diagram as shown Given
is a straight Assumed from diagram
is supp to If 2 angles form a straigt angle they are supp
is a straight Same as 2
is supp to Same as 3
If angles are supplementary to the same angle, they are congruent

16. Practice Problems
Given: is supp to
is supp to
Conclusion:

17. Works Cited
"Complementary, Supplementary, and Vertical Angles." Algrebra Labs. 29 May < _AnglesComplementarySupplementaryVertical.xml>.
Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougal Littell,