# Congruent Supplements and Complements

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Congruent Supplements and Complements
Section 2.4 By: Ellen Wildner

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

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

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

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…

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

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…

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

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…

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

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…

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.

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

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

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

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

Works Cited "Complementary, Supplementary, and Vertical Angles." Algrebra Labs. 29 May <http://www.algebralab.org/lessons/lesson.aspx?file=Geometry _AnglesComplementarySupplementaryVertical.xml>. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougal Littell,

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