Parallel Lines and Planes

Chapter 3 Parallel Lines and Planes page 72 Essential Question How can you apply parallel lines (planes) to make deductions?

Lesson 3-1 Definitions (page 73) Essential Question How can you apply parallel lines (planes) to make deductions?

1.Intersecting Lines - intersection occurs at ________ point. one LINES

2.PARALLEL LINES ( ||-lines ) : coplanar lines that do _______ intersect. not l m l || m

3.SKEW LINES : lines that are _____ coplanar. not r t r & t are skew lines

More SKEW LINES. y x x & y are skew lines

PLANES 1. Intersecting Planes - intersection is a _______. line

2.PARALLEL PLANES ( ||-planes ) : planes that do _______ intersect. not plane M || plane N plane M & plane N are horizonal planes

LINE and PLANE 1. Line Contained in a Plane - every point on line is in the plane.

2.Line Parallel to a Plane - the line and plane do not _____________. intersect

3. Line Intersects the Plane - the intersection occurs at one (1) _______. point

Turn to page 74 Trace or draw the diagram for your notes. Copy the proof if you wish. Given:plane X || plane Y plane Z intersects X in line l plane Z intersects Y in line m Theorem 3-1 Z If two parallel planes are cut by a third plane, then the lines are parallel.

TRANSVERSAL : a line that intersects 2 or more ___________ lines in different points. coplanar m n t Figure A t is a transversal

TRANSVERSAL : a line that intersects 2 or more ___________ lines in different points. coplanar x y z Figure B z is a transversal

Exterior angles : examples: ____________________________________ m n t Figure A ∠1∠1; ∠ 2 ; ∠ 7; ∠ 8 exterior

Exterior angles : examples: ____________________________________ x y z Figure B ∠9∠9; ∠ 12 ; ∠ 13; ∠ 16 exteriorexterior exteriorexterior

Interior angles : examples: ____________________________________ m n t Figure A ∠3∠3; ∠ 4 ; ∠ 5; ∠ 6 interior

Interior angles : examples: ____________________________________ x y z Figure B ∠ 10; ∠ 11 ; ∠ 14 ; ∠ 15 interiorinterior

Alternate Interior Angles : 2 nonadjacent interior angles on ____________ sides of the transversal. examples: ____________________________________ m n t Figure A ∠3∠3 and ∠ 5 ; ∠ 4and ∠ 6 opposite interior

Alternate Interior Angles : examples: ____________________________________ x y z Figure B ∠ 10 and ∠ 15 ; ∠ 14and ∠ 11 interiorinterior

Same Side Interior Angles : 2 interior angles on same side of a ________________. examples: ____________________________________ m n t Figure A ∠4∠4 and ∠ 5 ; ∠ 3and ∠ 6 transversal interior

Same Side Interior Angles : examples: ____________________________________ x y z Figure B ∠ 10 and ∠ 11 ; ∠ 14and ∠ 15 interiorinterior

Corresponding Angles : 2 angles in _____________________ positions relative to 2 lines. examples: _______________________________________________ m n t Figure A ∠ 1 & ∠ 5 corresponding ; ∠ 2 & ∠ 6 ; ∠ 3 & ∠ 7 ; ∠ 4 & ∠ 8

Corresponding Angles : examples: _______________________________________________ x y z Figure B ∠ 9 & ∠ 11 ; ∠ 10 & ∠ 12 ; ∠ 13 & ∠ 15 ; ∠ 14 & ∠ 16

Transversals t m n p

Using transversal t, name angle pairs. t m n p

Using transversal p, name angle pairs. t m n p

Assignment Written Exercises on pages 76 & 77 DO NOW: 1 to 17 odd number NOTE: We will do #19 & #21 in class! GRADED: 23 to 41 odd numbers How can you apply parallel lines (planes) to make deductions?

Parallel Lines cut by a Transversal For #18, #19, and #20 on page 76 use this diagram from your notes. Measure all the angles. What appears to be true? a b c

Parallel Lines cut by a Transversal Now let’s try this with lined notebook paper. The blue lines are all parallel.

Non-Parallel Lines cut by a Transversal Draw a diagram similar to the one on page 76, #21. 6 m ∠ 1 + m ∠ 2 = ? l m m ∠ 3 + m ∠ 4 = ? m ∠ 5 + m ∠ 6 = ? ∴ non-|| lines cut by a transversal ⇒ SSIA sum is constant.