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3.3/3.4 – Parallel Lines & Transversals. NO. YES. YES. NO. Transversals. Transversal: a line, ray or segment that intersects two or more coplanar lines, rays or segments each at a different point. Special Angle Relationships.
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NO YES YES NO Transversals • Transversal: a line, ray or segment that intersects two or more coplanar lines, rays or segments each at a different point
Special Angle Relationships When parallel lines are cut by a transversal, special angle relationships are formed. The following are those relationships.
Special Angle Relationships EXTERIOR INTERIOR EXTERIOR
1 2 3 4 6 5 7 8 Special Angle Relationships 3 & 6 and 4 & 5 are ALTERNATE INTERIOR ANGLES Alternate Interior Angles are CONGRUENT
1 2 3 4 6 5 7 8 Special Angle Relationships 1 & 8 and 2 & 7 are ALTERNATE EXTERIOR ANGLES Alternate Exterior Angles are CONGRUENT
1 2 3 4 6 5 7 8 Special Angle Relationships 3 & 5 and 4 & 6 are SAME SIDE INTERIOR ANGLES Same Side Interior Angles are SUPPLEMENTARY
Special Angle Relationships 1 2 3 4 3 & 7, 1 & 5, 2 & 6 and 4 & 8 are CORRESPONDING ANGLES 6 5 7 8 Corresponding Angles are CONGRUENT
1 2 3 4 6 5 7 8 Application 105
1 2 3 4 6 5 7 8 Application 47
Challenge! 1 113 2 11 10 3 4 5 12 13 70 15 14 6 7 8 16 9 17
1 2 3 4 6 5 7 8 Are n and m parallel? Why or why not? Application n 120 60 m t
1 2 3 4 6 5 7 8 Are n and m parallel? Why or why not? Application 60 n 60 m t
1 2 3 4 6 5 7 8 Are n and m parallel? Why or why not? Application n 120 m 121 s
1 2 3 4 6 5 7 8 Are n and m parallel? Why or why not? Application n 120 120 m r
1 2 3 4 6 5 7 8 Are n and m parallel? Why or why not? Application 60 n m 60 v