4.5 INTRO TO PARALLEL LINES

How can we recognize planes, transversals, pairs of angles formed by a transversal, and parallel lines?

DEFINITION: PARALLEL LINES

Two coplanar lines that do not intersect

UNDEFINED TERM: PLANEPLANEA surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface.A plane only has 2 dimensions.

Special Note: NON-Coplanar Lines are called Skew Lines

SYMBOLS FOR PARALLEL LINES

1

2

1 2

RECALL THE THREE UNDEFINED TERMS

DEFINITION: COPLANAR

Points, lines, and segments on the same plane.

Definition: NONCOPLANAR

Points, lines, and segments not on the same plane.

A

F

B

D

G

DEFINITION: TRANSVERSAL

A line that intersects two coplanar lines in two distinct points.

1

2

T Note that the lines are not necessarily parallel.

DEFINITIONS: OF SPECIAL ANGLES

12

34

56

7 8

Interior Angles – lie between the two ll lines (3, 4, 5, and 6)

Alternate Interior Angles – are on opposite sides of the transversal. (3 & 6 AND 4 and 5)

Same-Side Interior Angles – are on the same side of the transversal. (3 & 5 AND 4 & 6)

T

65

43

DEFINITIONS: MORE SPECIAL ANGLES

21

7 8

Exterior Angles – lie outside the two lines (1, 2, 7, and 8)

Alternate Exterior Angles – are on opposite sides of the transversal (1& 8 AND 2 & 7)

Corresponding Angles – same location, different intersections (2 & 6, 4 & 8, 1 & 5, 3 & 7)