Download 2.8 Proving Angle Relationships

2.8 Proving Angle Relationships
What you’ll learn:
1. To write proofs involving
supplementary and
complementary angles.
2. To write proofs involving
congruent and right angles.
Postulates
Postulate 2.10 – Protractor Postulate – angles
can be measured using a protractor.
Postulate 2.11 – Angle Addition Postulate
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
P
interior of PQS.
R
Q
S
Theorems
2.3 Supplement Theorem – If 2 s form a linear
pair, then they are supplementary s.
2.4 Complement Theorem – if the noncommon
sides of 2 adjacent s form a right , then the
s are complementary s.
2.5. Congruence of s is reflexive, symmetric, and
transitive.
Reflexive: AA
Symmetric: If AB, then BA
Transitive: If AB and BC, then AC.
2.6 Angles supplementary to the same angle or to
congruent angles are congruent.
More Theorems
2.7 Angles complementary to the same angle or to
congruent angles are congruent.
2.8 If 2 angles are vertical angles, then they are
congruent.
2.9 Perpendicular lines intersect to form 4 right
angles.
2.10 All right angles are congruent.
2.11 Perpendicular lines form congruent adjacent
angles
2-12 If 2 s are  and supplementary, then each 
is a right .
2-13 if 2  s form a linear pair, then they are right
s.
Don’t forget
Definition of supplementary angles – if 2 angles
are supplementary, they add to be 180.
Definition of complementary angles – if 2 angles
are complementary, they add to be 90.
Definition of congruent angles: if 2 angles are
congruent, they are equal in measure and
vice-versa.
Definition of angle bisector – an angle bisector
creates 2 congruent angles.
Definition of right angles – if an angle is right, its
measure is 90
Find the measure of each numbered
angle.
1.
3.
1
2
4
1
3
2
1=65, 2=?
2.
1
2
3
1=32, 2=?, 3=?
1=125, 2=?, 3=?,
4=?
4.
1
2
4
3
4=x-32, 2=175-2x
Sometimes, always, never
1. Supplementary angles are congruent.
sometimes
2. If 2 angles form a linear pair, then they are
complementary.
never
3. Two vertical angles are supplementary.
sometimes
4. Two angles that are congruent to the same
angle are congruent to each other.
always
Write a 2-column proof.
A
1
Given: ABC is a right angle. B
Prove: 1 and 2 are complementary angles
1.
2.
3.
4.
5.
ABC is a right angle.
mABC =90
mABC =m1+m2
90=m1+m2
1 and 2 are
complementary angles
2
C
Given
defn. right angles
Angle addition postulate
Substitution
Defn of comp. angles
Homework
p. 112
16-32 even, 38,
46-54 even