Download Geometry Fall 2014 Lesson 031 _Properties of Parallel Lines

1
Lesson Plan #31
Class: Geometry
Date: Friday November 12th, 2014
Topic: Properties of parallel lines (continued)
Aim: How do we use the properties of parallel lines?
Objectives:
Students will be able to use the properties of parallel lines.
HW #31:
Page 81 #’s 1-10
R
Recall the previously stated postulate “Through a
given point not on a given line, there exists one and
only one line parallel to the given line.”
Do Now:
Note:
B
1) Construct a line through point R that is parallel to AB
2)
A
3)
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Assignment #1:
1) Write the converse of the statement “If I live in New York City, then I live in New York State”
2) Write the converse of the statement “If two lines are cut by a transversal so that alternate interior angles are congruent, then
the two lines are parallel”
3) If a statement is true, is the converse of that statement always true?
4) Is the converse of the statement in (2) true or false?
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Let’s see if we can prove the converse of the theorem “If two planar lines are cut by a transversal so that alternate interior angles
are congruent, then the two lines are parallel”, namely “If two parallel lines are cut by a transversal, then the
alternate interior angles formed are congruent.”
Given:
Prove:
2
1
4
m
3
Let’s try a proof by contradiction:
5
6
7
8
n
Plan: Assume
Then draw a line through the vertex of angle 4 so it that it forms an angle
congruent to
. This would lead to congruent alternate interior angles, meaning
this new line is parallel to line n. But we already had one line (m) parallel to the
given line (n) through a point not on the line.
2
1
4
m
3
5
6
7
8
But this contradicts our previously stated postulate which states through a point not
on a given line, there is one and only one line parallel to the given line.
Theorem: If two parallel lines are cut by a transversal, then the alternate interior angles
formed are congruent.
Theorems that are converses of other previously stated theorems (presented without proof)



If two parallel lines are cut by a transversal, then the corresponding angles are congruent
If two parallel lines are cut by a transversal, then the two interior angles on the same side of the
transversal are supplementary
If a line is perpendicular to one of two parallel lines, it is perpendicular to the other.
Assignment #2:
Assignment #3:
n
3
Assignment #4: In your groups, complete the sample test questions
4
5
6
Sample Test Questions:
1)
2)
3)
4)
5)
6)