Download parallel lines

Properties of
Parallel Lines
Objectives:
Explore relationships of
the angles of parallel
lines cut by a transversal.
parallel lines
two or more co-planar lines that
do not intersect
Co-planar
lie on same plane
m//n // o
Are these two lines
parallel?
No - they intersect (cross).
Are these two lines
parallel?
No - they will intersect if
you extend the lines.
Are these two lines
parallel?
It sure looks like they are!
transversal –
a line that intersects 2 or more lines
Line n is a transversal.
It intersects lines a & b.
Is line r a transversal?
Yes - it intersects 3 lines.
When parallel lines are cut by a
transversal, these special
relationships are formed among
the angles!
corresponding angles – CA
two angles on the same side
of transversal and on the
same side of the parallel lines
Corresponding Angle Conjecture:
If two parallel lines are cut by a
transversal, then C.A.’s are congruent
alternate interior angles – AIA
angles that are on opposite
sides of transversal and
between the parallel lines
Alternate Interior Angle Conjecture:
If two parallel lines are cut by a
transversal, then A.I.A.’s are congruent.
alternate exterior angles –
AEA
angles that are on opposite
sides of transversal and not
between the parallel lines
Alternate Exterior Angle Conjecture:
If two parallel lines are cut by a
transversal, then A.E.A.’s are
congruent.
Sketch this diagram.
Write in the unknown
< measures.
Measure of
<1=?
Measure of < 2 =?
Measure of < 3 =?
Measure of
< 4 =?
Measure of < 5 =?
Measure of
< 6 =?
Measure of
< 7=?
You just found 7 angle
measures when you
were given only one
angle measure!
If AIA are congruent
then are lines m and n
parallel??