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WARM UP Look through pages 192-195 Write down the definitions of
– Transversals– Interior– Exterior– Alternate Interior Angles– Alternate Exterior Angles– Corresponding Angles
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4.5 Parallel lines
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Obj:recognize planes, Recognize transversals, identify the pairs of angles formed by a transversal,
recognize parallel lines.
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Plane:
•A surface with any two points connected by a line. There must be at least one point not on the line.
•Has only two dimensions, length and width (infinite)
•Has no thickness
Plane m
m
y
x
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Coplanar:
• Points that lie on the same plane (like collinear)
Non-coplanar:
• points that do not lie on the same plane
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Transversals:
• A line that intersects two coplanar lines in two distinct points. Not always parallel.
•Parts of a transversal:
•Exterior region
•Interior region
•Exterior region
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Transversals angles:
• alternate interior angles, angles on opposite sides of the transversal in the interior region
• alternate exterior angles, angles on opposite sides if the transversal in the exterior region
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• corresponding angles: angles in the same position in relation to the transversal
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12
34
56
78
Name the alternate interior angles.
Name the alternate exterior angles.
Name the corresponding angles.
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7m
n
k
1 23 4
5 68
When the two lines cut by the transversal are parallel, certain angles are congruent!
Given: lines n and m are parallel cut by transversal k
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m
n
k
1 23 4
5 68
Alternate interior angles are congruent
Alternate exterior angles are congruent
Corresponding angles are congruent
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m
n
k
1 23 4
5 68
Name the alternate interior angles
Name the alternate exterior angles
Name the corresponding angles
What other angles are congruent???
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Notice: if you know one angle in a set of transversal lines where two of the lines are parallel, you know all eight angles.
Given: <1 = 45degrees, name the other angles.
m
n
k
1 23 4
5 68
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Parallel lines:
• two coplanar lines that do not intersect. (equidistance apart)
• symbol ll or on lines > >
• segments and rays can also be parallel
• to be parallel, the lines MUST BE COPLANAR!
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Skew lines:
• Lines that never touch
• aren’t coplanar or parallel!