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Geometry
sections 3.1-3.2
Parallel Lines and Angle Pairs
Parallel Lines – Lines which are coplanar
and never intersect
Parallel Planes – Planes which never intersect
Skew Lines – Lines which are NOT coplanar
and never intersect
Transversal – A line which intersects two or
more coplanar lines. (The 2 lines may or may
not be parallel).
Angle pairs formed by transversals:
Corresponding Angles: angles which occupy the
same position in relation to the lines.
Alternate Interior Angles: angles which lie
inside the two lines, are on opposite sides of the
transversal, and are not a linear pair.
Alternate Exterior Angles: angles which lie
outside the two lines, are on opposite sides of
the transversal, and are not a linear pair.
Consecutive Interior Angles: angles which lie
inside the two lines and on the same side of the
transversal.
These pairs of angles are formed any time you have a transversal.
The other lines do not have to be parallel for the angle pairs to exist and be named!
Postulates and Theorems:
(These apply when the lines cut by the transversal are parallel.)
Postulate 15: If parallel lines are cut by a transversal, then pairs of corresponding angles are
congruent.
Theorem 3.1: If parallel lines are cut by a transversal, then pairs of alternate interior angles are
congruent.
Theorem 3.2: If parallel lines are cut by a transversal, then pairs of alternate exterior angles are
congruent.
Theorem 3.3: If parallel lines are cut by a transversal, then pairs of consecutive interior angles
are supplementary.
Students draw in diagrams from board
Ex 1).
Corresponding Angles
Alternate Exterior Angles
Ex 2).
Ex 3).
Ex 4).
Ex 5).
See Back
Alternate Interior Angles
Consecutive Interior Angles
Ex 6).
Ex 7).
Ex 8).