Download Line and Angle Relationships

Line and Angle Relationships
Parallel Lines and a Transversal
•Parallel lines: In geometry, two lines in a plane (a flat surface that
extends infinitely in all directions) that never intersect.
a
•Example-
b
•Notation:
•Transversal: A line that intersects at least two other lines. In the
example below, c is a transversal.
a
•Example-
b
c
If parallel lines are intersected by a
transversal, then…
•Interior angles lie inside the parallel lines.
•Examples:
•Exterior angles lie outside the parallel lines.
•Examples:
•Alternate interior angles are on opposite sides of the transversal and inside the
parallel lines. These angles are also congruent.
•Examples:
•Alternate exterior angles are on opposite sides of the transversal and outside the
parallel lines. These angles are also congruent.
•Examples:
•Corresponding angles are in the same position on the parallel lines in relation the
transversal. These angles are also congruent.
•Examples:
1
2
3 4
5
6
8 7
Intersecting Lines and Angles
•Vertical angles: The opposite angles formed when two lines intersect.
Vertical angles are congruent ( ).
•Example-
1
2
4
3
•Adjacent angles: Two angles that have the same vertex, share a
common side, and do not overlap.
•Example- In the above diagram,
(there are
more).
•Complementary angles: Two angles that have measures with a sum of
90°.
•Hint- Think corner when you see the word complementary to help
you remember the definition.
•Supplementary angles: Two angles that have measures with a sum of 180°.
•Hint- Think straight when you see the word supplementary to help you remember the
definition.
1
2
•Example:
•Perpendicular lines: Lines that intersect to form right angles.
•Example: