2-7 Prove Angle Pair Relationships
Geometry
Name ________________________
Date ________
Theorem 2.3 – Right Angle Congruence Theorem
1. From a previous section, which types of angles add up to 90o? _______________
2. From a previous section, which types of angles add up to 180o? ______________
Theorem 2.4 – Congruent Supplements Theorem
d
3
7
4
6 = 58o
5
m
2 = 58o
1
h
8
Use this diagram to answer the following questions.
1. Based on their measures, what can you say about  2 and  6? ________________
2. Which angles are supplementary to these two angles?
a.  2 supplements  _____
b.  6 supplements  _____
3. What are the measures of those two angles? Write it on the diagram.
4. Compare the two supplements from question 2, what can you say about their
measures? ___________________________
5. Generalize what must be true about supplements of congruent angles (hint: you could
put in an if-then statement)
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
6. What is another supplement for  2? ___________________
7. What is the measure of that angle? ___________________
8. Generalize what must be true about supplements of the same angle.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
2
Theorem 2.5 – Congruent Complements Theorem
J
M
T
P
Given: GKJ and MNK are a right angles
37o
53o
G
K
N
H
9. What is mJKN ? _____________
10. Fill in the blank: m JKT ____________ m MNP
11. Fill in the blanks
a. JKT _____________________ TKN (word not symbol)
b. MNP ____________________ PNH (word not symbol)
c. m JKT + m TKN = ___________
d. m MNP + m PNH = ___________
e. How do we know that m JKT + m TKN = m MNP + m PNH ?
_________________________________________________________
12. Based on what you’ve just found, fill in the blanks with the following words and
symbol (congruent, complements,  ):
Angles JKT and MNP are _________________ angles. Angles TKN and PNH
are _____________________ of JKT and MNP , respectively.
Therefore, TKN ____________ PNH .
13. Generalize the specific example above for any two angles:
_____________________________________________________________________
3
l
m
1
n
Given: 𝑙 ⊥ 𝑚, 𝑙 ⊥ 𝑛
Prove: ∠1 ≅ ∠2
2
E
D
Q
F
 ________ and  ________ are supplementary
These two angles are also called a _______________ ___________.
Postulate 12 –
4
Vertical Angles:
Theorem 2.6 –
 1 and  3 are vertical angles.
Prove: 1  3
Given:
4
1
3
2
Proof:
Statements
Reasons
1. m1  m4  180
1.
2. m3  m4  180
2.
3.
3.
m1  m4  m3  m4
4. m4  m4
4.
5. m1  m3
5.
6. 1  3
6.
qed
5