Transcript 7 2 Proving Parallel Lines

7-2 Proving Lines are Parallel
Objectives:
1. To use angle pair
relationships to
prove that two lines
are parallel
2. To construct parallel
lines with a compass
and straightedge
Assignment:
• P. 83: 12-16
• P. 87-88: 13-17
• Challenge Problems
Warm-Up
What is the converse of the Alternate
Exterior Angles Theorem?
If two parallel lines are cut by a transversal,
then pairs of alternate exterior angles are
congruent.
Is this converse necessarily true?
Objective 1
You will be able to use angle pair
relationships to prove that two lines
are parallel
Proving Lines Parallel
Converse of Same-Side Interior
Postulate
If two lines are cut by a transversal
so that same-side interior angles
are supplementary, 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 Corresponding Angles
Theorem
If two lines are cut by a transversal
so that corresponding angles are
congruent, then the lines are
parallel.
Example 1
Can you prove that lines a and b are
parallel? Explain why or why not.
Example 2
Find the value of x that makes m||n.
Example 3
Prove the Converse of the Alternate Interior
Angles Theorem.
Given: 3  6
Prove: l m
Example 4
Given: 1 and 3 are supplementary
2  3
Prove: RA TP
Example 5
Find the values of x and y so that l||m.
l
5x+3
m
10y+2
15y+6
2x-6
o
n
Objective 2
You will be able to construct parallel lines with a
compass and straightedge
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’.
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.
7-2 Proving Lines are Parallel
Objectives:
1. To use angle pair
relationships to
prove that two lines
are parallel
2. To construct parallel
lines with a compass
and straightedge
Assignment:
• P. 83: 12-16
• P. 87-88: 13-17
• Challenge Problems