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?

LINES one Intersecting Lines - intersection occurs at ________ point.

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

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

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

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

plane M & plane N are horizonal planes 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.

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

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

Theorem 3-1 Turn to page 74 Trace the diagram If two parallel planes are cut by a third plane, then the lines are parallel. Given: plane X || plane Y plane Z intersects X in line l plane Z intersects Y in line m Prove: l || m Z Turn to page 74 Trace the diagram And copy the proof in your notes.

TRANSVERSAL: a line that intersects 2 or more coplanar lines in different points. 1 4 3 m t is a transversal 5 6 n 8 7 t Figure A

TRANSVERSAL: a line that intersects 2 or more coplanar lines in different points. z is a transversal 12 11 10 9 15 16 14 13 z y x Figure B

Exterior angles: examples: ____________________________________ ∠1 ; ∠2 ; ∠7 ; ∠8 exterior 2 1 4 3 m 5 6 n 8 7 exterior t Figure A

Exterior angles: examples: ____________________________________ ∠9 ; ∠12 ; ∠13 ; ∠16 e x t r i o e x t r i o 12 11 10 9 16 15 14 13 z y x Figure B

Interior angles: examples: ____________________________________ ∠3 ; ∠4 ; ∠5 ; ∠6 2 1 4 3 m interior 5 6 n 8 7 t Figure A

Interior angles: examples: ____________________________________ ∠10 ; ∠11 ; ∠14 ; ∠15 i n t e r o 11 12 10 9 15 16 14 13 z y x Figure B

Alternate Interior Angles: 2 nonadjacent interior angles on opposite sides of the transversal. examples: ____________________________________ ∠3 and ∠5 ; ∠4 and ∠6 2 1 4 3 m interior 5 6 n 8 7 t Figure A

Alternate Interior Angles: examples: ____________________________________ ∠10 and ∠15 ; ∠14 and ∠11 i n t e r o 11 12 10 9 15 16 14 13 z y x Figure B

Same Side Interior Angles: 2 interior angles on same side of a transversal . examples: ____________________________________ ∠4 and ∠5 ; ∠3 and ∠6 2 1 4 3 m interior 5 6 n 8 7 t Figure A

Same Side Interior Angles: examples: ____________________________________ ∠10 and ∠11 ; ∠14 and ∠15 i n t e r o 11 12 10 9 15 16 14 13 z y x Figure B

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

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

Transversals t m 1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

Using transversal t, name angle pairs. 1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

Using transversal p, name angle pairs. 1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

How can you apply parallel lines (planes) to make deductions? Assignment Written Exercises on pages 76 & 77 RECOMMENDED: 1 to 17 odd numbers REQUIRED: 23 to 41 odd numbers How can you apply parallel lines (planes) to make deductions?