Transcript 3.3 Prove Lines Parallel

Warm-Up
What is the converse of the Corresponding
Angles Postulate?
If two parallel lines are cut by a transversal,
then pairs of corresponding angles are
congruent.
Is this converse necessarily true?
3.3 Prove Lines are Parallel
Objectives:
1. To use angle pair relationships to prove
that two lines are parallel
Copying an Angle
Draw angle A on your paper. How could you
copy that angle to another part of your
paper using only a
compass and a
straightedge?
Copying an Angle
1. Draw angle A.
Copying an Angle
2. Draw a ray with endpoint A’.
Copying an Angle
3. Put point of compass on A and draw an
arc that intersects both sides of the angle.
Label these points
B and C.
Copying an Angle
4. Put point of compass on A’ and use the
compass setting from Step 3 to draw a
similar arc on the ray.
Label point B’ where
the arc intersects
the ray.
Copying an Angle
5. Put point of compass on B and pencil on
C. Make a small arc.
Copying an Angle
6. Put point of compass on B’ and use the
compass setting from Step 5 to draw an
arc that intersects the
arc from Step 4.
Label the
new point
C’.
Copying an Angle
7. Draw ray A’C’.
Copying an Angle
Click on the
button to
watch a
video of the
construction.
Constructing Parallel Lines
Now let’s apply
the construction
for copying an
angle to create
parallel lines by
making
congruent
corresponding
angles.
Constructing Parallel Lines
1. Draw line l and
point P not on l.
Constructing Parallel Lines
2. Draw a
transversal
through point P
intersecting line l.
Constructing Parallel Lines
3. Copy the angle
formed by the
transversal and
line l at point P.
Constructing Parallel Lines
Click on the
image to
watch a
video of the
construction.
Proving Lines Parallel
Converse of Corresponding Angles
Postulate
If two lines are cut by a transversal
so that corresponding angles are
congruent, then the lines are
parallel.
Converse of Alternate Interior
Angles Theorem
If two lines are cut by a transversal
so that alternate interior angles
are congruent, then the lines are
parallel.
Proving Lines Parallel
Converse of Alternate Exterior
Angles Theorem
If two lines are cut by a transversal
so that alternate exterior angles
are congruent, then the lines are
parallel.
Converse of Consecutive Interior
Angles Theorem
If two lines are cut by a transversal
so that consecutive interior
angles are supplementary, then
the lines are parallel.
Example 1
Can you prove that lines a and b are
parallel? Explain why or why not.
No, not enough information
Yes, alt. ext angles
are congruent
Yes, corresponding
angles are congruent
Example 2
Find the value of x that makes m||n.
x=24
Example 3
Prove the Converse of the Alternate Interior
This proof has the angles
Angles Theorem.
numbered differently, but you get
the idea
Given: 3  6
Prove: l m
Example 4
Given: 1 and 3 are supplementary
2  3
Prove: RA TP
Do this is your
notebook. You can do
it. I BELIEVE in
you!!
Example 5
Find the values of x and y so that l||m.
l
5x+3
m
x=15
y=10
15y+6
2x-6
10y+2
o
n
Oh, My, That’s Obvious!
Transitive Property of
Parallel Lines
If two lines are parallel
to the same line, then
they are parallel to
each other.