Geometry 3 1 Lines and Transversals Parallel Lines

Geometry 3. 1 Lines and Transversals

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

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

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

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

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

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

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

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

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

Alternate Interior Angles(Alt. Int <‘s) n n Two nonadjacent interior angles on opposite sides of the transversal. What are the two pairs of Alt. Int. <‘s? t 1 3 5 7 2 4 6 8 <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) n Two interior angles on the same side of the n transversal. What are the two pairs of S. S. Int. <‘s? t 1 3 5 7 2 4 6 8 <3 and <5 <4 and <6 The lines do not need to be parallel for this to be true!

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

Finding a transversal n n n 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 B D 2 Angles 1 and 5 Transversal AE Angles 2 and 6 A 1 3 F E 4 5 6 C 7 8 Transversal BC Angles 4 and 7 Transversal EF

Sometimes, Always, or Never? n n n 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

n 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 n n 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