Download Section 2.6 Special Angles on Parallel Lines Notes

Section 2.6 Notes: Special Angles on Parallel Lines
Goals of the lesson:
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Explore relationships of the angles formed by a transversal cutting parallel lines
Learn new vocabulary
Develop inductive reasoning abilities, problem solving skills, and cooperative behavior.
Definitions from this section: transversal, corresponding angles, alternate interior angles, alternate exterior
angles, same side interior angles, parallel lines conjecture.
Homework: Review p. 128 - 131 and Do p. 131-134 #1-7, 9, 14-16, 19, 20 plus study for the quiz on
Section 2.1 and 2.4
Warm up:
1. Name all the Linear Pairs in the diagram on the right:
2. Name all the Vertical Angle pairs in the diagram on the right:
3. Name a pair of:
a. Alternate interior angles
b. Alternate exterior angles
c. Corresponding angles
d. Same side interior angles
What is a transversal?
Three new angle terms:
Corresponding angles: Angles that are in the exact same spot when cut by a transveral
Alternate interior angles: Angles that are inside of a Z pattern. They are on opposite sides of the transversal
on the interior of the two lines.
Alternate exterior angles: Angles that are on the outside of a Z pattern. They are on opposite sides of the
transversal, on the exterior of the two lines.
We will look at Geometer’s sketch pad together, to determine what is true about corresponding angles,
alternate interior angles and alternate exterior angles.
Corresponding angles conjecture: If two parallel lines are cut by a transversal, then corresponding angles are
Alternate interior angles conjecture: If two parallel lines are cut by a transversal, then alternate interior angles
are
Alternate exterior angles conjecture: If two parallel lines are cut by a transversal, then alternate exterior
angles are
Parallel lines conjecture: If two parallel lines are cut by a transversal, then corresponding angles are
______________, alternate interior angles are ___________________, and alternate exterior angles are
______________
How do we know these conjectures are true?
Use a deductive argument to prove the alternate interior angles conjecture is true.
Statement
Reason
What about the converse of the parallel lines conjecture? What is it? Is it true?
If two lines are cut by a transversal AND alternate interior angles are congruent, corresponding angles are
congruent and alternate exterior angles are congruent, then the two lines are parallel.
We will use sketch pad to explore that as well.
Converse of the parallel lines conjecture:
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are
_______________.
If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are
_______________.
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are
_______________.
One more angle pair:
Same side interior angles: Angles that FORM a C or backwards C and are on the INSIDE. So they are on the
same side of the transversal, on the INSIDE of the parallel lines.
Relationship with Same-side interior angles:
If two parallel lines are cut by a transversal, then same side interior angles are _______________________.
Converse: If same side interior angles are ________________________, then lines are parallel.
Try on your own:
10. Find x.
11. Find x.