Lines and Angles

Geometry

Chapter 3, Section 1

Notes What does it mean for two lines to be parallel?

Parallel lines: Lines that do not intersect and are coplanar.

What about lines that don’t intersect and aren’t coplanar?

Skew Lines: Lines that do not intersect and are not coplanar.

What does it mean for two planes to be parallel? Parallel Planes: planes that do not intersect. Example: the planes containing the ceiling and floor are

parallel

Notes Parallel 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. Parallel lines have the same slope (e.g. slope of 3 and 3) Tilted at the same angle

Perpendicular Postulate: If 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. Perpendicular lines have slopes that are negative reciprocals

(e.g. 4 and – 1/4) At 90 degrees from each other

m

P

k

Q

Notes Transversal: a line that intersects two or

more lines in a plane at different points. E.g. Line c is a transversal to lines a and b. Line b is a transversal to which two other lines?

a & c How about line a?

b & c When a transversal

intersects two lines,

how many angles are

formed? 8 angles are formed

a

cb

Notes Angles formed by a transversal.

We give certain pairs of these angles special names. Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8 Exterior Angles: 1, 2, 7, & 8 Interior Angles: 3, 4, 5, 6 Alternate Exterior Angles: 1 & 7 ; 2 & 8 Alternate Interior Angles: 3 & 5 ; 4 & 6 Consecutive Interior Angles: 4 & 5 ; 3 & 6

2

5

13

7

4

86

Notes Symbols for parallel in statements and figures

The symbol ll means is parallel to The pink arrows on lines PQ and RS indicate that they

are parallel.

Angle Pair Names Activity Using about ¼ of a piece of binder paper, draw three lines so that one intersects

two of the others. Color the exterior angles all one color Color the interior angles all one color Label the exterior and interior angles

Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others. Color each pair of corresponding angles a different color. Label this quarter sheet of paper “corresponding angles.”

Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others. Color each pair of alternate exterior angles a different color. Color each pair of alternate interior angles a different color. Label this quarter sheet “alternate exterior and interior angles.”

Using the final ¼ of a piece of binder paper, draw three lines so that one intersects two of the others. Color each pair of consecutive interior angles a different color. Label this quarter sheet “consecutive interior angles.