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Teacher Notes
Angle Relationships
Objective:
 To identify and use adjacent, vertical, complementary, supplementary,
and linear pairs of angles and perpendicular lines.

To determine what information can and can not be assumed from a
diagram
Definitions:
Perpendicular lines – special intersecting lines that form right angles.
Adjacent angles – angles in the same plane that have a common vertex and
common side, but no common interior points.
Vertical angles – two nonadjacent angles formed by two intersecting lines.
Linear pair – adjacent angles whose noncommon sides are opposite rays.
Supplementary angles – two angles whose measures have a sum of 180˚.
Complementary angles – two angles whose measures have a sum of 90˚.
Notes:
Vertical angles are congruent. (This is the symbol for congruent, .)
The sum of the measures of the angles in a linear pair is 180˚.
 means perpendicular m  n is read m is perpendicular to n.
 lines intersect to form four right angles.
If a line is perpendicular to a plane then that line is perpendicular to every line in
the plane that it intersects.
M
N
O
Q
From the picture above,
You CAN assume:
 All points shown are coplanar.
 L, P, and Q are collinear.



PM, PN, PO and LQ intersect at
P.
P is between L and Q.
N is in the interior of angle MPO.

Angle LPQ is a straight angle.
P
L
You CAN NOT assume:
 PN is perpendicular to PM
 Angle QPO is congruent to angle
LPM
 LP is congruent to PQ



PQ is congruent to PO
Angle QPO is congruent to angle
OPN
Angle OPN is congruent to angle
LPM



Angle LPM and angle MPN are
adjacent angles
Angle LPN and angle NPQ are a
linear pair.
Angle QPO and angle OPL are
supplementary

PO is congruent to PN

PN is congruent to PL
M
N
O
Q
P
L
With these additional markings, you can now assume a few more things that
could not be assumed from the first picture.
 PN is perpendicular to PM
 QP is congruent to PL
 Angle QPO is congruent to angle MPL
Examples:
J
G
I
K
H
Find the value of x.
Angle GIJ = 9x – 4 and angle JIH = 4x – 11
Angle GIJ = 16x – 20 and angle KIH = 13x + 7
1
2 3
5
4
Identify each pair of angles as adjacent, vertical, complementary,
supplementary, and/or as a linear pair.
Angle 1 and angle 2
Angle 1 and angle 4
Angle 3 and angle 4
Angle 1 and angle 5