Angle Relationships Formed by Intersecting Lines
Glossary 3
Definition of Vertical Angles:
1. The opposite angles formed by two intersecting lines.
2. The nonadjacent angles formed by two intersecting lines.
Statement
1 & 3 are opposite angles formed
Justification
Definition of Vertical Angles
If two angles are vertical angles, then they have equal
measures (or congruent).
Statement
1
by intersecting lines
1 & 3 are non-adjacent angles
Vertical Angles Theorem
Definition of Vertical Angles
3
m 1 m 3
Justification
Vertical Angles Theorem
Vertical Angles Theorem
formed by intersecting lines
Definition of Linear Pair:
1. Adjacent angles formed when two lines intersect.
2. A pair of adjacent angles whose non common sides are opposite rays
.
Statement
1 & 2 are a linear pair
JL and JK
are opposite rays
Justification
Definition of Linear Pair
6 & 3 are supplementary
If two angles form a linear pair, then they are supplementary.
Statement
1 & 2 are supplementary
Justification
Linear Pair Theorem
Definition of Linear Pair
Definition of Supplementary Angles
Two angles whose measures have a sum of 180°
Statement
m 6  m 3  180 °
Linear Pair Theorem:
Justification
varies
Definition of Supplementary
Statement
6 & 3 are supplementary
Justification
varies
m 6  m 3  180
Definition of Supplementary
Definition of Complementary Angles
Two angles whose measures have a sum of 90°
How to show that angles are supplementary
using Linear Pairs:
Statement
m 6 and m 3
form a linear pair
6 & 3 are supplementary
m 6  m 3  180 °
Justification
Definition of Linear Pair
Linear Pair Theorem
Definition of Supplementary
Equal Measure Linear Pair Theorem:
If two intersecting lines form a linear pair of angles with equal
measures, then the lines are perpendicular.
Definition opposite rays: two rays that have a common
endpoint and form a straight line.
Definition adjacent angles:
1. A pair of angles that share a vertex and one side but do not overlap.
2. Two coplanar angles that have a common side, same vertex, don’t
overlap, and no interior points in common
Definition of Straight Angle: An angle whose measure is equal
to 180°
Definition of Angle Bisector:
A line or ray that divides an angle in half.
Definition of Segment Bisector:
A line or ray that divides a line segment in half.
Definition of Midpoint
A point on a line segment is a midpoint if and only if
it divides the segment into two equal parts.
The halfway point of a line segment
Angle Bisector Theorem:
If a point is on the bisector of an angle,
then it is equidistant from the two sides of the angle.
Angle Bisector Converse:
If a point is in the interior of an angle and is equidistant from
the sides of the angle,
then it lies on the bisector of the angle.