Geometry 3.1 Lines and Transversals

Parallel Lines // Lines Coplanar lines that do not intersect j // k j k

Skew Lines Noncoplanar lines that do not intersect line g is skew to line h g and h are skew lines g h

// and Skew Lines What are some // lines in the diagram? What are some skew lines in the diagram? E A B C D H G F

Segments and rays… …contained in // lines are also parallel.. B. A. C. D AB // CD

Are segments QP and RS parallel? They do not intersect! But they are parts of lines PQ and RS, which are not parallel.. Thus, the answer is no! Q P RS

// Planes…do not intersect What are some parallel planes in the diagram? Example: Plane ABCD // Plane EFGH E A B C D H G F

A line and a plane are // if they do not intersect! Examples? Example: Plane ABCD // EF E A B C D H G F

Theorem If two parallel planes are cut by a third plane, then the lines of intersection are parallel. j k j // k

Transversal A line that intersects two or more coplanar lines in different points. t t is a transversal The lines do not need to be parallel to have a transversal !

Interior Angles and Exterior Angles Exterior angles 1, 2, 7, and 8. Interior angles 3, 4, 5, and 6. t The lines do not need to be parallel for this to be true!

Alternate Interior Angles(Alt. Int <‘s) Two nonadjacent interior angles on opposite sides of the transversal. What are the two pairs of Alt. Int. <‘s? t <3 and <6 <4 and <5 The lines do not need to be parallel for this to be true!

Same Side Interior Angles(S.S. Int <‘s) Two interior angles on the same side of the transversal. What are the two pairs of S.S. Int. <‘s? t <3 and <5 <4 and <6 The lines do not need to be parallel for this to be true!

Corresponding Angles(Corr. <‘s) Two angles in corresponding positions relative to the two lines. What are the four pairs of Corr. <‘s? t <1 and <5 <2 and <6 <3 and <7<4 and <8 The lines do not need to be parallel for this to be true!

Finding a transversal Trace each < identified. The line you touch twice is the transversal. Name the two lines and the transversal between angles…It helps to draw an isolated picture A B C D Angles 1 and 5 Transversal AE E Angles 2 and 6 Transversal BC F Angles 4 and 7 Transversal EF

Sometimes, Always, or Never? When there is a transversal of 2 lines, the 3 lines are _________ coplanar. Answer: Always 2 Lines that are not coplanar __________ intersect. Answer: Never 2 Planes // to the same line are _________ // to each other. Answer: Sometimes

Review Sheet

Please open your books to page 76 #4, 6, 12, 18, 24, 26, 34, 38 4) Alt. Int <‘s 6) Corr. <‘s 8) Lines PS, QR, and transversal SQ 12) Corr. <‘s 18) Corr. <‘s are congruent 24) GH, ED, KJ 26) CDJI and GHIJKL 34) Sometimes 38) Sometimes

HW P. 76 – 77, #1-41 odd, skip 19 and 21 Self Test P. 65 Odds Vocab Quiz tomorrow, Chapter 2 Test Friday Ch. Review Today