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# Geometry Section 3-2 1112

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### Geometry Section 3-2 1112

1. 1. SECTION 3-2 ANGLES AND PARALLEL LINESWednesday, December 14, 2011
2. 2. ESSENTIAL QUESTIONS HOW DO YOU USE THEOREMS TO DETERMINE THE RELATIONSHIPS BETWEEN SPECIFIC PAIRS OF ANGLES? HOW DO YOU USE ALGEBRA TO FIND ANGLE MEASUREMENTS?Wednesday, December 14, 2011
3. 3. POSTULATES AND THEOREMS CORRESPONDING ANGLES POSTULATEWednesday, December 14, 2011
4. 4. POSTULATES AND THEOREMS CORRESPONDING ANGLES POSTULATE IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CORRESPONDING ANGLES IS CONGRUENT.Wednesday, December 14, 2011
5. 5. POSTULATES AND THEOREMS CORRESPONDING ANGLES POSTULATE IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CORRESPONDING ANGLES IS CONGRUENT. ∠1 ≅ ∠5Wednesday, December 14, 2011
6. 6. POSTULATES AND THEOREMS ALTERNATE INTERIOR ANGLES THEOREMWednesday, December 14, 2011
7. 7. POSTULATES AND THEOREMS ALTERNATE INTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE INTERIOR ANGLES IS CONGRUENT.Wednesday, December 14, 2011
8. 8. POSTULATES AND THEOREMS ALTERNATE INTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE INTERIOR ANGLES IS CONGRUENT. ∠4 ≅ ∠6Wednesday, December 14, 2011
9. 9. POSTULATES AND THEOREMS CONSECUTIVE INTERIOR ANGLES THEOREMWednesday, December 14, 2011
10. 10. POSTULATES AND THEOREMS CONSECUTIVE INTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CONSECUTIVE INTERIOR ANGLES IS SUPPLEMENTARY.Wednesday, December 14, 2011
11. 11. POSTULATES AND THEOREMS CONSECUTIVE INTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF CONSECUTIVE INTERIOR ANGLES IS SUPPLEMENTARY. ∠4 AND ∠5 ARE SUPPLEMENTARYWednesday, December 14, 2011
12. 12. POSTULATES AND THEOREMS ALTERNATE EXTERIOR ANGLES THEOREMWednesday, December 14, 2011
13. 13. POSTULATES AND THEOREMS ALTERNATE EXTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE EXTERIOR ANGLES IS CONGRUENT.Wednesday, December 14, 2011
14. 14. POSTULATES AND THEOREMS ALTERNATE EXTERIOR ANGLES THEOREM IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN EACH PAIR OF ALTERNATE EXTERIOR ANGLES IS CONGRUENT. ∠2 ≅ ∠7Wednesday, December 14, 2011
15. 15. EXAMPLE 1 IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO YOUR ANSWER. a. m∠2 b. m∠3 c. m∠6Wednesday, December 14, 2011
16. 16. EXAMPLE 1 IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO YOUR ANSWER. a. m∠2 51°; VERTICAL ANGLES WITH ∠4 b. m∠3 c. m∠6Wednesday, December 14, 2011
17. 17. EXAMPLE 1 IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO YOUR ANSWER. a. m∠2 51°; VERTICAL ANGLES WITH ∠4 b. m∠3 129°; SUPPLEMENTARY ANGLES WITH ∠4 c. m∠6Wednesday, December 14, 2011
18. 18. EXAMPLE 1 IN THE FIGURE, m∠4 = 51°. FIND THE MEASURE OF EACH ANGLE. GIVE A JUSTIFICATION TO YOUR ANSWER. a. m∠2 51°; VERTICAL ANGLES WITH ∠4 b. m∠3 129°; SUPPLEMENTARY ANGLES WITH ∠4 c. m∠6 51°; ALTERNATE INTERIOR ANGLES WITH ∠4Wednesday, December 14, 2011
19. 19. EXAMPLE 2 USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR THE ANSWER FOR EACH MEASURE.Wednesday, December 14, 2011
20. 20. EXAMPLE 2 USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR THE ANSWER FOR EACH MEASURE. m∠1 = 125°; VERTICAL WITH ∠2Wednesday, December 14, 2011
21. 21. EXAMPLE 2 USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR THE ANSWER FOR EACH MEASURE. m∠1 = 125°; VERTICAL WITH ∠2 m∠3 = 55°; CONSECUTIVE INTERIOR WITH ∠2Wednesday, December 14, 2011
22. 22. EXAMPLE 2 USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR THE ANSWER FOR EACH MEASURE. m∠1 = 125°; VERTICAL WITH ∠2 m∠3 = 55°; CONSECUTIVE INTERIOR WITH ∠2 m∠4 = 125°; CONSECUTIVE INTERIOR WITH ∠3Wednesday, December 14, 2011
23. 23. EXAMPLE 2 USE THE FIGURE, IN WHICH a||b, m∠2 = 125°, AND c||d||e, TO FIND THE MEASURE OF EACH NUMBERED ANGLE. PROVIDE A REASON FOR THE ANSWER FOR EACH MEASURE. m∠1 = 125°; VERTICAL WITH ∠2 m∠3 = 55°; CONSECUTIVE INTERIOR WITH ∠2 m∠4 = 125°; CONSECUTIVE INTERIOR WITH ∠3 m∠5 = 55°; SUPPLEMENTARY WITH ∠4Wednesday, December 14, 2011
24. 24. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x.Wednesday, December 14, 2011
25. 25. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x. 2x − 10 = x + 15Wednesday, December 14, 2011
26. 26. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x. 2x − 10 = x + 15 −x −xWednesday, December 14, 2011
27. 27. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x. 2x − 10 = x + 15 −x +10 −x +10Wednesday, December 14, 2011
28. 28. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x. 2x − 10 = x + 15 −x +10 −x +10 x = 25Wednesday, December 14, 2011
29. 29. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. a. IF m∠2 = 2x − 10 AND m∠6 = x + 15, FIND x. 2x − 10 = x + 15 −x +10 −x +10 x = 25 SINCE THE ANGLES ARE CORRESPONDING, THEY ARE CONGRUENT, MEANING THEY ARE EQUAL.Wednesday, December 14, 2011
30. 30. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y.Wednesday, December 14, 2011
31. 31. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y. 4(y − 25) + 4y = 180Wednesday, December 14, 2011
32. 32. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y. 4(y − 25) + 4y = 180 4y − 100 + 4y = 180Wednesday, December 14, 2011
33. 33. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y. 4(y − 25) + 4y = 180 4y − 100 + 4y = 180 8y − 100 = 180Wednesday, December 14, 2011
34. 34. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y. 4(y − 25) + 4y = 180 4y − 100 + 4y = 180 8y − 100 = 180 8y = 280Wednesday, December 14, 2011
35. 35. EXAMPLE 3 USE THE FIGURE TO FIND THE INDICATED VARIABLE. EXPLAIN YOUR REASONING. b. IF m∠7 = 4(y − 25) AND m∠1 = 4y, FIND y. 4(y − 25) + 4y = 180 4y − 100 + 4y = 180 8y − 100 = 180 8y = 280 y = 35Wednesday, December 14, 2011
36. 36. CHECK YOUR UNDERSTANDING CHECK OUT PROBLEMS 1-10 ON PAGE 181.Wednesday, December 14, 2011
37. 37. PROBLEM SETWednesday, December 14, 2011
38. 38. PROBLEM SET P. 181 #11-35 ODD “YOU CAN FOOL TOO MANY OF THE PEOPLE TOO MUCH OF THE TIME.” - JAMES THURBERWednesday, December 14, 2011