Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 90 For Ex. 1 56 therefore 2 must equal… 90 56 34 Review Continued • Supplementary Angles – 2 angles are supplementary if the sum of their measures is180 For Ex. 1 112 therefore 2 must equal… 180 112 68 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 1 is supplementary to A , and2 is also supplementary to A 1 A 2 Therefore we can prove that… 1 2 Sample Problem Thm 4. Given: 1 is supp. to 2 3 is supp. to 4 1 4 1 4 3 Prove: 2 3 Statements 2 Reasons 1. 1 is supp. to 2 2. 3 is supp. to 4 1. Given 2. Given 3. 1 4 3.Given 4. 2 3 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 A is supp. to B C is supp. toD And that B D B A C D Therefore we can prove that… A C Sample Problem Thm. 5 Given: 5 supp. of 6 7 supp. of 8 6 7 Conclusion: 5 8 Statements 5 6 1. Given 2.7 supp. of 8 2. Given 4. 5 6 7 8 7 8 Reasons 1.5 supp. of 3. 6 3. Given 4. 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 A comp B and A comp C C A B Therefore we can prove that… B C Sample Problem Thm. 6 Given: 1 comp 2 2 comp3 Conclusion: 1 2 3 3 Statements 1. 1 comp 2 2.2 comp 3 3 3. 1 1 Reasons 1. Given 2. Given 3. 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 1 comp 2 and3 comp 4 1 3 4 2 Therefore we can prove that… 3 1 Sample Problem Thm. 7 Given: 1 comp to 2 3 comp to 4 1 3 Conclusion: 2 4 Statements 1. 1 comp to 2 2.3 comp to 4 3. 1 3 4. 2 4 1 4 2 3 Reasons 1. Given 2. Given 3. Given 4. If angles are complementary to congruent angles, then they are congruent. Practice Problems Given: E is comp to G HFG is comp to G E H Conclusion:HFG E F Statements G Reason 1. E is comp to HFG 1. Given 2.HFG is comp to 2. Given 3. E HFG 3. If angles are complementary to the same angle they are congruent Practice Problems Applying skills Given: is comp to 3 4 = 131 2 1 8 a. 3 = 49 b. 6 = 131 c. 5 = 49 d. 2 = 41 e. 1 = 139 f. 8 = 41 g. 7 = 139 2 7 4 3 6 5 Practice Problems G H Given: Diagram as shown Prove: HFE GFJ F E J Statements 1. Diagram as shown Reasons 1. Given 2.EFG is a straight 2. Assumed from diagram 3.HFE is supp to HFG 3. If 2 angles form a straigt angle they are supp 4.HFJ is a straight 4. Same as 2 5.GFJ is supp to HFG 5. Same as 3 6.HFE GFJ 6. If angles are supplementary to the same angle, they are congruent Practice Problems Given:1 is supp to 3 2 is supp to 4 1 2 Conclusion: 3 4 2 1 3 4 Works Cited "Complementary, Supplementary, and Vertical Angles." Algrebra Labs. 29 May 2009 <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, 1997. 7681.