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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: StatementsReasons 1. is supp. to1. Given 2. is supp. to2. 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 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: StatementsReasons 1. supp. of 1. Given 2. supp. of 2. Given 3. 3. Given 4. 4. 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 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: StatementsReasons 1. comp 1. Given 2. comp 2. Given 3. 3. 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. Therefore we can prove that… For ex. It is given that comp and comp

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Sample Problem Thm. 7 Given: comp to comp to Conclusion: Statements Reasons 1. comp to 1. Given 2. comp to 2. Given 3. 3. Given 4. 4. 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 1. is comp to 1. Given 2. is comp to 2. Given 3. 3. 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 c. = 49 d. = 41 e. = 139 f.= 41 g.= 139

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Practice Problems Given: Diagram as shown Prove: Statements Reasons 1. Diagram as shown 1. Given 2. is a straight 2. Assumed from diagram 3. is supp to 3. If 2 angles form a straigt angle they are supp 4. is a straight 4. Same as 2 5. is supp to 5. Same as 3 6. 6. 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 2009. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1997. 76- 81.

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