parallel lines again
TRANSCRIPT
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Properties of Parallel Lines
Objectives:Explore relationships of the angles of parallel lines cut by a transversal.
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parallel l ines - two or more co-planar lines that do not intersect
Co-planar - lie on same plane
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mn o
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No - they intersect (cross).
Are these two lines parallel?
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No - they will intersect if you extend the lines.
Are these two lines parallel?
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It sure looks like they are!
Are these two lines parallel?
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transversal - a line that intersects 2 or more lines
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Line n is a transversal. It intersects line a & b.
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Is line r a transversal?
Yes - it intersects 3 lines.
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corresponding angles - two angles on the same side of transversal and on the same side of the parallel lines
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< 1 and 1 5 are corresponding angles. List
the other 3 pairs of corresponding c ’s.
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alternate interior angles - angles that are on opposite sides of transversal and between the parallel lines
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< 3 and 3 6 are alternate interior angles. List the other pair of A.I.A.’s.
4 & 5
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alternate exterior angles - angles that are on opposite sides of transversal and not between the parallel lines
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< 1 and 1 8 are alternate exterior angles. List the other pair of A.E.A.’s.
2 & 7
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When parallel lines are cut by a transversal, there are special relationships among the angles formed…..let’s investigate!
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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
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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
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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
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Sketch this diagram. Write in unknown angle measures.
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Measure of M 1 =?
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Measure of M 1 =?
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Measure of M 2 =?
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Measure of M 2 =?
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Measure of M 3 =?
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Measure of ∠ 3 =?
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Measure of M 4 =?
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Measure of M 4 =?
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Measure of M 5 =?
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Measure of M 5 =?
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Measure of M 6 =?
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Measure of M 6 =?
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Measure of M 7=?
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Measure of M 7=?
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You just found 7 angle measures when you were given only one angle measure!
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You know that if two lines are parallel, then the transversal will form congruent alternate interior angles.
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Do you think line m is parallel to line n? Why?