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Proving Angle
Relationships
Protractor Postulate
- Given AB and a number r between 0
and 180, there is exactly one ray with
endpoint A, extending on either side of
AB, such that the measure of the angle
formed is r.
Angle Congruence

Congruence of angles is reflexive, symmetric, and
transitive:
1.
Reflexive
1  1
2.
Symmetric
If 1  2, then 2  1
3.
Transitive
If 1  2 and 2  3,
then 1  3
Angle Addition Postulate
P
R
Q


S
If R is in the interior of PQS,
then mPQR + mRQS = mPQS
If mPQR + mRQS = mPQS, then R
is in the interior of PQS
Angle Addition
A
If mABD  44 and
mABC  88 , find mDBC.
B
D
C
mABD  mDBC  mABC
44  mDBC  88
mDBC  44
Right Angle Theorems

List 3 - 5 facts that you observe about
the perpendicular lines below:
Right Angle Theorems

Perpendicular lines intersect to form four right angles

All right angles are congruent

Perpendicular lines form congruent adjacent angles

If two angles are congruent and supplementary, then
each angle is a right angle

If two congruent angles form a linear pair, then they are
right angles
Theorems

Supplementary Theorem – if two
angles form a linear pair, then they are
supplementary angles.

Complementary Theorem – if the noncommon sides of two adjacent angles
form a right angle, then the angles are
complementary angles.
Theorems
2.6 Angles supplementary to the same angle or
to congruent angles are congruent.
2.7 Angles complementary to the same angle or
to congruent angles are congruent.
2.8 Vertical angles theorem: If two angles are
vertical angles, then they are congruent.
Supplementary Angles

Angles supplementary to the same angle or to
congruent angles are congruent

s suppl. to same  or  s are 

Example:
• m1 + m2 = 180
• m2 + m3 = 180
• Then, 1  3
2
1
3
Complementary Angles

Angles complementary to the same angle or to
congruent angles are congruent

s compl. to same  or  s are 

Example:
• m1 + m2 = 90
• m2 + m3 = 90
• Then, 1  3
1
2
3