Parallel and Skew Lines Concept 16 lar cu

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Parallel and Skew Lines Concept 16

Parallel and Skew Lines Concept 16

lar cu di en rp Pe Skew Parallel

lar cu di en rp Pe Skew Parallel

Parallel Lines: two or more lines in the same plane that never intersect. Parallel

Parallel Lines: two or more lines in the same plane that never intersect. Parallel Planes: two or more planes that never intersect. Skew Lines: two or more lines that lie in different planes that never intersect (not parallel). Perpendicular Lines: two lines that intersect to form 4 right angles. Perpendicular Planes: two planes that intersect to form right angles all along the intersection.

NO Yes NO

NO Yes NO

Plane EFGH Planes: ABCD, EFGH, EFBA, CDHG

Plane EFGH Planes: ABCD, EFGH, EFBA, CDHG

Concept 17 Angle pairs and transversals

Concept 17 Angle pairs and transversals

 • Transversal – a line intersected by two or more lines at different

• Transversal – a line intersected by two or more lines at different locations. • Same Side Exterior Angles – Same Side Ext. – angles on same side of transversal and outside the lines being intersected.

Alternate Interior Angles Alt. Int. – angles on opposite sides of the transversal and

Alternate Interior Angles Alt. Int. – angles on opposite sides of the transversal and in between the two lines being intersected.

Alternate Exterior Angles Alt. Ext. – angles on opposite sides of the transversal and

Alternate Exterior Angles Alt. Ext. – angles on opposite sides of the transversal and outside the two lines being intersected.

Corresponding Angles – angles on the same side of transversal and same side of

Corresponding Angles – angles on the same side of transversal and same side of intersected line.

Same Side Interior Angles Same Side Int. – angles on same side of transversal

Same Side Interior Angles Same Side Int. – angles on same side of transversal and in between the lines being intersected.

Same Side Exteior Angles Same Side Ext. – angles on same side of transversal

Same Side Exteior Angles Same Side Ext. – angles on same side of transversal and outside the lines being intersected.

Classify each set of angles. 1 and 5 Corresponding Angles 2. 8 and 11

Classify each set of angles. 1 and 5 Corresponding Angles 2. 8 and 11 Same Side Interior Angles 3. 9 and 6 Alternate Exterior Angles 4. 3 and 6 Same Side Exterior Angles 5. 8 and 12 Corresponding Angles 6. 7 and 5 None 7. 2 and 11 Alternate Interior Angles 8. 2 and 6 Corresponding Angles

Use the following picture to identify each pair of angles as: corresponding, alternate interior,

Use the following picture to identify each pair of angles as: corresponding, alternate interior, alternate exterior, same side interior, same side exterior, or none. Then name which line is the transversal for each pair. 1. 1 and 7 Corresponding Angles 2. 6 and 1 3. 8 and 4 Same Side Exterior Angles Alternate Interior Angles 4. 6 and 2 Alternate Exterior Angles 5. 1 and 4 None 6. 8 and 6 Corresponding Angles 7. 6 and 2 Alternate Exterior Angles 8. 3 and 4 Same Side Interior Angles

Use the following picture to identify each pair of angles as: corresponding, alternate interior,

Use the following picture to identify each pair of angles as: corresponding, alternate interior, alternate exterior, same side interior, or none. Then name which line is the transversal for each pair. 9. 1 and 9 Transversal: line A, Corresponding Angles 10. 6 and 3 Transversal: line C, Alternate Interior Angles 11. 15 and 4 Transversal: line B, Alternate Exterior Angles 12. 11 and 10 Transversal: line D, Same Side Interior Angles 13. 9 and 7 None 14. 5 and 9 Transversal: line A, Same Side Interior Angles 15. 12 and 4 Transversal: line B, Corresponding Angles 16. 3 and 16 Transversal: line B, Alternate Exterior Angles 17. 1 and 16 None 18. 10 and 15 Transversal: line D, Alternate Interior Angles

Tell which postulates (or theorems) you used. 19. In the figure, m 11 =

Tell which postulates (or theorems) you used. 19. In the figure, m 11 = 51. Find m 15. 20. In the figure, m 11 = 51. Find m 16. 21. If m 2 = 125, find m 3. 22. If m 2 = 125, find m 4.

In the figure, m∠ 3 = 102. Find the measure of each angle. 23.

In the figure, m∠ 3 = 102. Find the measure of each angle. 23. ∠ 5 = 24. ∠ 6 = 25. ∠ 11 = 26. ∠ 7 = 27. ∠ 15 = 28. ∠ 14 =

In the figure, m∠ 9 = 80 and m∠ 5 = 68. Find the

In the figure, m∠ 9 = 80 and m∠ 5 = 68. Find the measure of each angle. Tell which postulate(s) or theorem(s) you used. 29. ∠ 12 = 30. ∠ 1 = 31. ∠ 4 = 32. ∠ 3 = 33. ∠ 7 = 34. ∠ 16 =

35. If m 5 = 2 x – 10, and m 7 = x

35. If m 5 = 2 x – 10, and m 7 = x + 15, find x. 36. If m 4 = 4(y – 25), and m 8 = 4 y, find y. 37. If m 1 = 9 x + 6 and m 2 = 2(5 x – 3) find x. 38. Use the information from #37 and m 3 = 5 y + 14 to find y.