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SUBJECT MATTER: PROPERTIES OF PARALLEL LINES Pacing: Objective: To prove theorems about parallel lines 2 days To use properties of parallel lines to find angle measures Standards G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems. G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries. Warm Up: HSAP Review The equation C = $0.05m + 4.95 represents the cost (C) of a long distance telephone call m minutes. What does the rate of change represent in this situation? a. the initial charge for a call b. the cost of a long distance call c. the number of minutes of the call d. the cost per Postulate 3 - 2 - 1 Corresponding Angle Postulate POSTULATE HYPOTHESIS If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. CONCLUSION ∠1 ≅ ∠3 ∠2 ≅ ∠4 ∠5 ≅ ∠7 ∠6 ≅ ∠8 Example 1 Using the Corresponding Angles Postulate Find each angle measure. A. 𝑚∠𝐴𝐵𝐶 B. 𝑚∠𝐷𝐸𝐹 C. 𝑚∠𝑄𝑅𝑆 Theorems: Parallel Lines and Angle Pairs THEOREM 3 -2 -2 HYPOTHESIS CONCLUSION Alternate Interior Angles Theorem ∠1 ≅ ∠3 If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent 3 -2 -3 ∠2 ≅ ∠4 Alternate Exterior Angles Theorem ∠5 ≅ ∠7 If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent 3 -2 -4 ∠6 ≅ ∠8 Same-Side Interior Angles Theorem 𝑚∠1 + 𝑚∠4 = 1800 If two parallel lines are cut by a transversal, then the pairs of sameside interior angles are supplementary 𝑚∠2 + 𝑚∠3 = 1800 Example 2 Finding Angle Measures Find each angle measure. A. 𝑚∠𝐸𝐷𝐹 B. 𝑚∠𝑇𝑈𝑆 C. 𝑚∠𝐴𝐵𝐷 Example 3 Finding Angle Measures In the figure, 𝑛 ⃡∥𝑚 ⃡ , 𝑚∠4 = 50 and 𝑚∠16 = 80. Find the measure of each angle. A. ∠8 = _______________ B. ∠5 = _______________ C. ∠2 = _______________ D. ∠1 = _______________ E. ∠6 = _______________ F. ∠3 = _______________ G. ∠12 = _______________ H. ∠13 = _______________ I. ∠9 = _______________ J. ∠10 = _______________ K. ∠15 = _______________ L. ∠17 = _______________ Classwork Name: ____________________________________ Period: __________________ Date: _______________ Find each angle measure. 1. 𝑚∠𝐽𝐾𝐿 5. 𝑚∠𝐸𝐶𝐹 6. 𝑚∠𝐷𝐶𝐸 2. 𝑚∠𝐵𝐸𝐹 7. 𝑚∠𝐸𝐷𝐺 3. 𝑚∠1 4. 𝑚∠𝐶𝐵𝑌 8. 𝑚∠𝐵𝐷𝐺 In the figure at the right 𝑚 ∥ 𝑛, 𝑚∠4 = 590 and 𝑚∠15 = 770. Find the measure of each angle. 9. ∠3 = 10. ∠5 = 11. ∠13 = 12. ∠9 = 13. ∠15 = 14. ∠7 = 15. ∠8 = 16. ∠12 = 17. ∠16 = 18. ∠17 = HW: Do # 7 - 17 on page 153 Name: ____________________________________ Period: __________________ Date: _______________ Find each angle measure. 1. 𝑚∠𝐾𝐿𝑀 2. 𝑚∠𝑉𝑌𝑋 3. 𝑚∠𝐴𝐵𝐶 4. 𝑚∠𝐸𝐹𝐺 5. 𝑚∠𝑃𝑄𝑅 6. 𝑚∠𝑆𝑇𝑈 In the figure at the right, 𝑝 ⃡∥ 𝑞 ⃡, 𝑚∠1 = 107 and 𝑚∠11 = 48. Find the measure of each angle. 7. ∠3 = 8. ∠5 = 9. ∠13 = 10. ∠9 = 11. ∠15 = 12. ∠7 = 13. ∠8 = 14. ∠12 = 15. ∠16 =