Warm ups
Choose the plane parallel to
plane MNR.
Choose the segment skew to MP.
Classify the relationship
between <1 and <5.
Classify the relationship
between <3 and <8.
Classify the relationship
between <4 and <6.
3-2 ANGLES AND
PARALLEL LINES
Objective: Use theorems to determine
relationships between specific pairs of angles.
Use algebra to find angle measurements.
Concept
Example 1
A. In the figure, m<11 = 51.
Find m<15. Tell which
postulates (or theorems)
you used.
<15 is congruent to <11 Corresponding Angles Postulate
m<15 = m<11
Definition of congruent angles
m<15 = 51
Substitution
Answer: m<15 = 51
Use Corresponding Angles Postulate
Example 1
B. In the figure, m<11 = 51.
Find m<16. Tell which
postulates (or theorems)
you used.
<15
@
@
<16
@
m<16
=
<16
m<16
<15
Vertical Angles Theorem
<11
Corresponding Angles
Postulate
<11
Transitive Property
m<11 Definition of congruent
angles
= 51
Answer: m<16 = 51
Use Corresponding Angles Postulate
Substitution
Example 1a
A. In the figure, a || b and
m<18 = 42. Find m<22.
A. 42
B. 84
C. 48
D. 138
Example 1b
B. In the figure, a || b and
m<18 = 42. Find m<25.
A. 42
B. 84
C. 48
D. 138
Parallel Lines and Angle Pairs
Alternate Interior Angles Theorem
Example 2
FLOOR TILES The diagram
represents the floor tiles in
Michelle’s house. If m<2 = 125,
find m<3.
@
<2
Theorem
m<2 = m<3
125 = m<3
<3 Alternate Interior Angles
Definition of congruent angles
Substitution
Answer: m<3 = 125
Use Theorems about Parallel Lines
Example 2
FLOOR TILES The diagram
represents the floor tiles in
Michelle’s house. If m<2 = 125,
find m<4.
A. 25
B. 55
C. 70
D. 125
Example 3
A. ALGEBRA If m<5 = 2x – 10,
and m<7 = x + 15, find x.
@
<5
Postulate
m<5 = m<7
2x – 10 = x + 15
x – 10 = 15
x = 25
Answer: x = 25
Find Values of Variables
<7 Corresponding Angles
Definition of congruent angles
Substitution
Subtract x from each side.
Add 10 to each side.
Example 3
B. ALGEBRA If m<4 = 4(y – 25),
and m<8 = 4y, find y.
<8
@
<6
Corresponding Angles
Postulate
m<8 = m<6
Definition of congruent
angles
4y = m<6
Find Values of Variables
Substitution
Example 3 continued
m<6 + m<4 = 180
Supplement Theorem
4y + 4(y – 25) = 180
Substitution
4y + 4y – 100 = 180
Distributive Property
8y = 280
Add 100 to each side.
y = 35
Divide each side by 8.
Answer: y = 35
Find Values of Variables
Try with a Mathlete
A. ALGEBRA If m<1 = 9x + 6,
m<2 = 2(5x – 3), and
m<3 = 5y + 14, find x.
A. x = 9
B. x = 12
C. x = 10
D. x = 14
TOO
B. ALGEBRA If m<1 = 9x + 6,
m<2 = 2(5x – 3), and
m<3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24
Concept
Homework
• Pg. 183 # 11 – 19, 25, 27, 29, 36, 43, 46