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**Congruent Supplements and Complements**

Section 2.4 By: Ellen Wildner

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**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

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**Review Complementary Angles**

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

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**Review Continued Supplementary Angles**

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

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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…

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**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

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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…

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**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

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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…

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**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

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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…

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**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.

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**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

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**Practice Problems Applying skills Given: is comp to = a. = 49 b. = 131**

d = 41 e = 139 = 41 = 139

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**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

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

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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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