Geometry CPA Unit 2 Summative #2 PDF

______ Name: ___________________________________ Date: ______________________ Block: _________ Geometry CPA Unit 2 Summative #2 90 Show all work to receive full credit. I should be able to follow your train of though...

______ Name: ___________________________________ Date: ______________________ Block: _________ Geometry CPA Unit 2 Summative #2 90 Show all work to receive full credit. I should be able to follow your train of thought. You will be graded on both the correctness of your methods as well as on the accuracy of your final answer. Leave all answers in simplified improper fraction form, where applicable. Good Luck J Use the diagram below. For each pair of given angles, identify the special angle pair and the transversal. If the angles are not a special angle pair, write “NONE and leave transversal question blank.” [4 points each] 1. ∠2 and ∠6 ___________________________________________, transversal _________________ 2. ∠1 and ∠12 ____________________________________________, transversal _________________ 3. ∠10 and ∠13 ____________________________________________, transversal _________________ 4. ∠6 and ∠15 ___________________________________________, transversal _________________ 5. Are lines p and q parallel? Circle yes or no. State the theorem/postulate to explain your reasoning. p Circle one: YES or NO q Theorem/Postulate: _________________________________________ For questions #6–8, Solve for the given variable(s) and state what postulate(s) or theorem(s) you used to arrive at your solution. 6. Assume y || z. x = ______________ Theorem/Postulate _________________________ 7. Assume q || r. x = ______________ Theorem/Postulate _________________________ 8. Assume l || m. x = _______________ Theorem/Postulate _________________________ y = _______________ Theorem/Postulate _________________________ For questions 9–12 refer to the diagram below to answer the questions below (treat each problem separately). Use proper notation when stating the parallel lines. If there are no parallel lines write “NONE” and leave the postulate/theorem blank. [4 points each] 9. Given that ∠8 ≅ ∠19, which lines, if any, are parallel? a. _______________________ b. Postulate/Theorem: _______________________________________ 10. Given that ∠13 ≅ ∠15, which lines, if any, are parallel? a. _______________________ b. Postulate/Theorem: ________________________________________ 11. Given that ∠14 𝑎𝑛𝑑 ∠18 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦, which lines, if any, are parallel? a. _______________________ b. Postulate/Theorem: ________________________________________ 12. Given that ∠11 ≅ ∠6, which lines, if any, are parallel? a. _______________________ b. Postulate/Theorem: ________________________________________ 13. Complete the proof. [18 points] Given: ∠2 𝑎𝑛𝑑 ∠4 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 Prove: 𝑙 ‖ 𝑚 Statement Reason 1. ∠2 𝑎𝑛𝑑 ∠4 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 1. Given 2. 2. 3. ∠4 𝑎𝑛𝑑 ∠5 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 3. 4. 4. Definition of Supplementary Angles 5. 𝑚∠2 + 𝑚∠4 = 𝑚∠4 + 𝑚∠5 5. 6. 𝑚∠2 = 𝑚∠5 6. 7. 7. 8. 𝑙 ‖ 𝑚 8. 14. Complete the proof. [12 points] Given: a║b and c║d Prove: 𝑚∠1 = 𝑚∠2 Statement Reason 1. a║b and c║d 1. Given 2. ∠1 ≅ ∠3 2. 3. 3. 4. 4. 5. 𝑚∠1 = 𝑚∠2 5.