Parallel lines and Transversal ( Math 8 )
- 3. _ _ _ _ _ _ _ _ P O O P P A T I E S O P P O S I T E
- 4. L I N E _ _ _ _ A L P H N E I T
- 5. _ _ _ _ _ _ _ _ L A L P P A T L E R P A R A L L E L
- 6. T R I A N G L E _ _ _ _ _ _ _ _ T A L G N A I L E R
- 7. A N G L E _ _ _ _ _ M N R E A G C E L
- 10. Parallel Lines -lines that never intersect
- 12. When two parallel lines are cut by a third line, the third line is called________________. TRANSVERSAL m n l It is a line that intersects two or more lines at different points. 1 2 3 4 5 6 7 8
- 13. Vertical Angles Two angles are vertical angles if and only if the sides of one angle are opposite rays to the sides of the other. Ð1 and Ð4 Ð6 and Ð7
- 14. Supplementary Angles Two angles are supplementary if and only if the sum of their measures is 180 degrees. Ð1 and Ð2 Ð6 and Ð8
- 15. Alternate Interior Angles Two angles in the interior of the parallel lines, and on opposite sides of a transversal. Ð3 and Ð6 Ð4 and Ð5
- 16. Alternate Exterior Angles Two angles in the exterior of the parallel lines, and on opposite sides of a transversal Ð1 and Ð8 Ð2 and Ð7
- 17. Corresponding Angles Two angles, one in the interior and one in the exterior, that are on the same side of the transversal and on the same position Ð1 and Ð5 Ð4 and Ð8
- 18. Same-side Interior Angles -two angles that are on the same side of the transversal and on the interior of the two lines Ð3 and Ð5
- 19. Same-side Exterior Angles -two angles that are on the same side of the transversal and on the exterior of the two lines Ð2 and Ð8
- 22. Identify each pair of angles as corresponding,alternate interior, alternate exterior, or consecutive interior angles.
- 35. A B D C Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD Interior Exterior Exterior
- 36. Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD A D B C
- 37. Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Parallel lines transversal Non-Parallel lines transversal Interior Exterior Exterior Interior Exterior Exterior
- 38. Parallel Lines and Transversals Transversal - A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. t m k j Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.
- 39. interior INTERIOR –The space INSIDE the 2 lines EXTERIOR -The space OUTSIDE the 2 lines exterior exterior
- 40. Special Angle Relationships Interior Angles <3 & <6 are Alternate Interior angles <4 & <5 are Alternate Interior angles <3 & <5 are Same Side Interior angles <4 & <6 are Same Side Interior angles 1 4 2 6 5 7 8 3 Exterior Angles <1 & <8 are Alternate Exterior angles <2 & <7 are Alternate Exterior angles <1 & <7 are Same Side Exterior angles <2 & <8 are Same Side Exterior angles Interior Exterior Exterior
- 41. Special Angle Relationships WHEN THE LINES ARE PARALLEL ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY 1 4 2 6 5 7 8 3 If the lines are not parallel, these angle relationships DO NOT EXIST. Interior Exterior Exterior
- 42. Corresponding Angles & Consecutive Angles Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5, 3 7, 4 8 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 43. Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent. ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Line M B A Line N D E L P Q G F Line L
- 44. Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º m1 +m7 = 180º, m2 +m8 = 180º 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 45. The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. A pair of interior angles lie on the same side of the transversal. The measures of interior angles in each pair add up to 1800 . Interior Angles Line M B A Line N D E L P Q G F Line L 600 1200 1200 600 ÐBPQ + ÐEQP = 1800 ÐAPQ + ÐDQP = 1800 Interior Exterior Exterior
- 46. Alternate Interior/Exterior Angles • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 47. Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M B A Line N D E L P Q G F Line L ÐBPQ = ÐDQP ÐAPQ = ÐEQP Pairs of alternate angles are congruent. Two pairs of alternate angles are formed.
- 48. Let’s Practice m<1=120° Find all the remaining angle measures. 1 4 2 6 5 7 8 3 60° 60° 60° 60° 120° 120° 120° 120°
- 49. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 120° 120° 60° 60° 40° 60° 60° 180-(40+60)= 80° 80° 80° 80° 100° 100°