1

Pairs of Lines

2

Parallel Lines

• Parallel lines are coplanar lines that do not intersect.• Arrows are used to indicate lines are parallel.• The symbol used for parallel lines is ||.

AB CD���������������������������������������� ���

DC

BA

In the above figure, the arrows show that line AB is parallel to line CD.

With symbols we denote, .

3

PERPENDICULAR LINES

• Perpendicular lines are lines that intersect to form a right angle.

• The symbol used for perpendicular lines is . • 4 right angles are formed.

m

nIn this figure line m is perpendicular to line n.

With symbols we denote, m n

4

OBLIQUE LINES

• Oblique lines are lines that intersect, but do NOT form a right angle.

5

Skew Lines and Parallel Planes

• Two lines are skew if they do not intersect and are not in the same plane (not coplanar).

Ex: are skew.

• All planes are either parallel or intersecting.

• Parallel planes are two planes that do not intersect.

CG and EF���������������������������������������� ���

H

E

G

DC

BA

F

Ex: Plane ABC and Plane EFG

are parallel planes

6

Examples:

1. Name all segments that are parallel to2. Name all segments that intersect 3. Name all segments that are skew to4. Name all planes that are parallel to plane BCG.

Answers:5. Segments BC, FG, & EH.6. Segments DH, DC, AE & AB.7. Segments CG, BF, FE, & GH.8. Plane ADH.

ADAD

AD

H

E

G

DC

BA

F

7

Example:

1) What are the lines parallel to CD?  2) What lines are perpendicular to CD?  3) What lines are skew to CD?  4) Name the parallel plane to CDA.  5) Name the plane perpendicular to CDA.