Download Note Sheet 2-8

June 30, 2013
Geometry 2-8 Proving Angle Relationships
Postulate 2.10: Protractor Postulate: Given any angle, the
measure can be assigned a value between 0 and 180.
Postulate 2.11: Angle Addition Postulate: Point D is in the
interior of ⦛ABC if and only if m⦛ABD + m ⦛DBC = m⦛ ABC.
D
A
B
6
7
C
⦛6 and ⦛7 form a linear
pair. If m⦛ 6 = 3x + 32
and m ⦛7 = 5x + 12, find
m ⦛6 and m⦛ 7.
3x + 32 + 5x + 12 = 180
8x + 44 = 180
8x = 136
x = 17
m⦛6 = 3(17) + 32 = 83
m⦛7 = 5(17) + 12 = 97
A
B
1
2
3
C
Find m⦛3 if m⦛1 = 23 and m⦛ABC = 131.
m⦛1 + m ⦛ 2 + m ⦛3 = m⦛ABC
23 + 90 + m ⦛3 = 131
m ⦛3 = 18
Theorem 2.3: Supplement Theorem: If two angles form a
linear pair, then they are supplementary angles.
Theorem 2.4: Complement Theorem: If the noncommon
sides of two adjacent angles form a right angle, then the
angles are complementary angles.
Theorem 2.5: Properties of Angle Congruence: Congruence
of angles is reflexive, symmetric, and transitive.
Our next two theorems are closely related.
Theorem 2.6: Congruent Supplements Theorem: Angles that
are supplementary to the same angle or to congruent angles
are congruent.
Theorem 2.7: Congruent Complements Theorem: Angles that
are complementary to the same angle or to congruent angles
are congruent.
Theorem 2.8: Vertical Angles Theorem: If two angles are
vertical angles, then they are congruent.
Theorem 2.11: Perpendicular lines form congruent adjacent
angles.
We will close out this lesson with a few theorems that pertain
only to right angles.
Theorem 2.12: If two angles are congruent and
supplementary, then both angles are right angles.
Theorem 2.9: Perpendicular lines intersect to form 4 right
angles.
Theorem 2.10: All right angles are congruent.
Theorem 2.13: If two congruent angles form a linear pair,
then they are right angles.