parallel lines lesson 4.5. objective: recognize planes and transversals, identify the pairs of...
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Parallel LinesLesson 4.5
Objective:Recognize planes and
transversals, identify the pairs of angles formed by a transversal and recognize parallel lines.
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
Coplanar:
• Points that lie on the same plane (like collinear).Non-coplanar:
• Points that do not lie on the same plane.
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
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.
• Corresponding Angles: angles in the same position in relation to the transversal.
12
34
56
78
Name the alternate interior angles.
Name the alternate exterior angles.
Name the corresponding angles.
2 & 76 & 3
1 & 8 5 & 4
1 & 3, 2 & 4, 5 & 7, 6 & 8
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
m
n
k
1 23 4
5 68
Alternate interior angles are congruent.
Alternate exterior angles are congruent.
Corresponding angles are congruent.
7
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???
7
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 = 45°name the other angles.
m
n
k
1 23 4
5 687
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!
Skew lines:
• Lines that never touch aren’t coplanar or parallel!