IDENTIFY P

AIRS OF LINES

AND ANGLES

S E C T I ON 3

. 1- 3 . 2

DEFINITIONSTwo lines are parallel lines if they do not intersect and are

coplanar. In other words , parallel lines do not intersect and run in the same direction.

Two lines are skew lines if they do not intersect and are not coplanar. In other words, skew lines do not intersect but don’t run in the same direction.

Two planes that do not intersect are called parallel planes.

DEFINITIONSPerpendicular lines are lines that intersect to form a right

angle.

Perpendicular planes are planes that intersect to form a right angle.

POSTULATESParallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Perpendicular PostulateIf there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

ANGLESA transversal is a line that intersects two or more coplanar

lines at different points.

Two angles are corresponding angles if they have corresponding positions.

Two angles are alternate interior angles if they lie between the two lines and on opposite sides of the transversal.

ANGLESTwo angles are alternate exterior angles if they lie outside the

two lines and on opposite sides of the transversal.

Two angles are consecutive interior angles if they lie between the two lines and on the same side of the transversal.

Two angles are consecutive exterior angles if they lie outside the two lines and on the same side of the transversal.

CORRESPONDING ANGLES POSTULATETwo lines cut by a transversal are parallel if and only if the

pairs of corresponding angles are congruent.

ALTERNATE INTERIOR ANGLES THEOREMTwo lines cut by a transversal are parallel if and only if the

pairs of alternate interior angles are congruent.

ALTERNATE EXTERIOR ANGLES THEOREMTwo lines but by a transversal are parallel if and only if the

pairs of alternate exterior angles are congruent.

CONSECUTIVE INTERIOR ANGLES THEOREMTwo lines cut by a transversal are parallel if and only if the

pairs of consecutive interior angles are supplementary.

EXAMPLEFind each numbered angle.

EXAMPLEFind the value of x.

EXAMPLEFind the value of x. The picture may not be drawn to scale.

(3x + 5)o

(7x – 15)o

ASSIGNMENT

p. 129: 3-8, 11-18p. 135: 3-12