parallel lines
TRANSCRIPT
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
mn o
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!
Are these two lines parallel?
transversal - a line that intersects 2 or more lines
Line n is a transversal. It intersects line a & b.
Is line r a transversal?
Yes - it intersects 3 lines.
corresponding angles - two angles on the same side of transversal and on the same side of the parallel lines
1 and 5 are corresponding angles. List the other 3 pairs
of corresponding ’s.
alternate interior angles - angles that are on opposite sides of transversal and between the parallel lines
3 and 6 are alternate interior angles. List the other pair of A.I.A.’s.
4 & 5
alternate exterior angles - angles that are on opposite sides of transversal and not between the parallel lines
1 and 8 are alternate exterior angles. List the other pair of A.E.A.’s.
2 & 7
When parallel lines are cut by a transversal, there are special relationships among the angles formed…..let’s investigate!
Compare the measures of pairs of corresponding angles…what do you see? C-17a Corresponding Angle Conjecture:If two parallel lines are cut by a transversal, then C.A.’s are ___________. congruent
Compare the measures of pairs of alternate interior angles…what do you see? C-17b Alternate Interior Angle Conjecture:If two parallel lines are cut by a transversal, then A.I.A.’s are ___________.
congruent
Compare the measures of pairs of alternate exterior angles…what do you see? C-17c 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 unknown angle measures.
Measure of 1 =?
Measure of 1 =?
Measure of 2 =?
Measure of 2 =?
Measure of 3 =?
Measure of 3 =?
Measure of 4 =?
Measure of 4 =?
Measure of 5 =?
Measure of 5 =?
Measure of 6 =?
Measure of 6 =?
Measure of 7=?
Measure of 7=?
You just found 7 angle measures when you were given only one angle measure!
You know that if two lines are parallel, then the transversal will form congruent alternate interior angles.
Do you think line m is parallel to line n? Why?