Parallel lines Section 3-1

3 line relationships Parallel lines – coplanar lines that never intersect Intersecting lines – coplanar lines that share one point Skew lines – noncoplanar lines

2 more items Parallel planes – 2 planes that never intersect (spacing remains even) A line and a plane are parallel – if they never intersect

Theorem 3-1 If 2 parallel planes are cut by a third plane, then the lines of intersection will be parallel If the first two planes are parallel, then the red lines are parallel.

Transversals Transversal – a line that intersects two or more coplanar lines in different points 1 2 A transversal is a route from one line to another 4 3 5 6 7 8 When two lines are cut by a transversal, there are 8 angles formed

Interior and Exterior Angles Interior angles – the angles between the two lines Exterior angles – the angles outside the two lines 1 2 4 3 5 6 8 7

Angle Pairs with Two Lines Cut by a Transversal 1 2 4 3 When we refer to an angle pair, we will use one angle from each of the two lines being cut by the transversal One from here And one from here 5 6 8 7

Corresponding Angles Lie in the same position with regard to the lines and the transversal. 2, 6 1, 5 3, 7 4, 8 1 2 4 3 5 6 8 7

Alternate Interior Angles (also called opposite interiors) Interior angles on opposite sides of the transversal 4, 6 3, 5 1 2 4 3 5 6 8 7

Same-side Interior Angles (also called consecutive interiors) Interior angles on the same side of the transversal 3, 6 4, 5 1 2 4 3 5 6 8 7

Alternate Exterior Angles Exterior angles on opposite sides of the transversal 1, 7 2, 8 1 2 4 3 5 6 8 7

Name the special angle pair for the given angles Name the special angle pair for the given angles. (One of these has no relationship) 1.) <1 & <5 2.) <10 & <15 3.) <7 & <13 4.) <16 & <8 5.) <11 & <10 6.) <2 & <7 7.) <7 & <14 8.) <9 & <13 9.) <2 & <9 10.) <14 & <6 11.) <16 & <13 12.) <10 & <7 13.) <11 & <15 1 3 5 6 2 4 7 8 9 10 13 14 11 12 15 16