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Unit Plan: Parallel Lines and Planes

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Mark Headen

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Transcript of Unit Plan: Parallel Lines and Planes

EDCI 536
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 . . .
Full transcript