Teaching & Learning Measurement & Geometry

Parallel Lines and Planes

by: Mark D. Headen

Concordia University

Portland, Oregon

May 25, 2013

**PARALLEL LINES AND PLANES**

EDCI 536

Teaching & Learning Measurement & GeometryParallel Lines and Planesby: Mark D. Headen Concordia UniversityPortland, OregonMay 25, 2013

LESSON OBJECTIVES

- Distinguish between intersecting

lines, parallel lines,

perpendicular

lines

and

skew lines.

- State and apply the theorem about the intersecting of

two parallel

planes

by a third plane.

- Identify the angles formed when

two lines

are cut by a

transversal.

- State and apply the postulates and theorems about

parallel lines.

- State and apply the theorems about

parallel

and

perpendicular

to a given

line through a point outside the line.

Perpendicular

Skew

Parallel

There are three types of lines . . .

Parallel Lines and Planes

by: Mark D. Headen

Parallel Lines:

two lines that lie in

the same plane and

they do not intersect

are called

parallel lines.

Example:

(real life example)

Perpendicular Lines:

Two lines that intersect to form

form right angles.

Example:

(real life example)

(symbol for perpendicular)

(symbol for parallel)

Skew Lines:

are lines that do not intersect and are not on the same

plane.

PQ and VU are skew lines

(real life example)

Transversal:

In a plane, a transversal is a line that

intersects two other lines in two

different points.

transversal

(real life example)

UNDERSTANDING ANGLES

it's vertical !

corresponding?

No! same side.

alternate exterior!?

alternate interior.

duh? adjacent!

I don't know.

Caution!

Vertical Angles:

are two nonadjacent angles formed by two intersecting lines.

Thm. 2-3:

Vertical Angles are congruent.

(real life example)

Example:

Notice !

Alternate Interior Angles:

Two angles that lie on opposite sides of a transversal between the two lines that the transversal intersects.

Example:

(real life example)

Halt!

Thm. 2-4:

If two lines are cut by a transveral and one pair of alternate interior angles are congruent, then the other pair of alternate interior angles are congruent.

Same Side Interior:

Two angles that lie on the same side of a transversal between the two lines tha t the transversal intersects.

(The sum of the measures of same side interiors equals 180 degrees.)

measure of angle └3 + measure of angle └5 =180º

measure of angle 4 + measure of angle 6 =180º

real life example

Warning!

Corresponding Angles:

Two angles that lie on the same side of a transversal, in corresponding

positions with respect to the two lines that the transversal intersects.

Thm. 2-5

If two lines are cut by a transversal and one pair of corrponding angles are congruent, then all pairs of corresponding angles are congruent.

(real life example)

Precautions

Adjacent Angles:

Two angles in a plane that have a common vertex and a common side, but no common interior points.

Example:

angle 1 and angle 2 are adjacent angles

Example:

Example:

(real life example)

Reference

Jurgensen, R. (1992). Geometry. Boston, MA: Houghton Mifflin Co.

**New York's Brooklyn Bridge**

Recapping Key Concepts

vertical angles

are equal

What are perpendicular lines?

A. Lines that add together to measure 180º.

B. Lines that do not intersect.

C. Two lines that intersect to form a right angle.

A. Lines that add together to measure 180º.

B. Lines that do not intersect.

C

.

Two lines that intersect to form a right angle.

Answer

let's look at an example . . .