LESSON 3–2
Angles and Parallel Lines
Five-Minute Check (over Lesson 3–1)
TEKS
Then/Now
Postulate 3.1: Corresponding Angles Postulate
Example 1: Use Corresponding Angles Postulate
Theorems: Parallel Lines and Angle Pairs
Proof: Alternate Interior Angles Theorem
Example 2: Real-World Example: Use Theorems about
Parallel Lines
Example 3: Find Values of Variables
Theorem 3.4: Perpendicular Transversal Theorem
Over Lesson 3–1
Choose the plane parallel to
plane MNR.
A. RST
B. PON
C. STQ
D. POS
Over Lesson 3–1
Choose the segment skew to MP.
___
A. PM
___
B. TS
___
C. PO
___
D. MQ
Over Lesson 3–1
Classify the relationship
between 1 and 5.
A. corresponding angles
B. vertical angles
C. consecutive interior
angles
D. alternate exterior
angles
Over Lesson 3–1
Classify the relationship
between 3 and 8.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. consecutive interior
angles
Over Lesson 3–1
Classify the relationship
between 4 and 6.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. vertical angles
Over Lesson 3–1
Which of the following segments
is not parallel to PT?
A. OS
B. TS
C. NR
D. MQ
Targeted TEKS
G.6(A) Verify theorems about angles formed by the
intersection of lines and line segments, including
vertical angles, and angles formed by parallel lines cut by a
transversal and prove equidistance between the endpoints of a
segment and points on its perpendicular bisector and apply
these relationships to solve problems.
Mathematical Processes
G.1(A), G.1(G)
You named angle pairs formed by parallel lines
and transversals.
• Use theorems to determine the relationships
between specific pairs of angles.
• Use algebra to find angle measurements.
Use Corresponding Angles Postulate
A. In the figure, m11 = 51.
Find m15. Tell which
postulates (or theorems)
you used.
15  11
Corresponding Angles Postulate
m15 = m11
Definition of congruent angles
m15 = 51
Substitution
Answer: m15 = 51
Use Corresponding Angles Postulate
B. In the figure, m11 = 51.
Find m16. Tell which
postulates (or theorems)
you used.
16  15
Vertical Angles Theorem
15  11
Corresponding Angles
Postulate
16  11
Transitive Property ()
m16 = m11 Definition of congruent
angles
m16 = 51
Answer: m16 = 51
Substitution
A. In the figure, a || b and
m18 = 42. Find m22.
A. 42
B. 84
C. 48
D. 138
B. In the figure, a || b and
m18 = 42. Find m25.
A. 42
B. 84
C. 48
D. 138
Use Theorems about Parallel Lines
FLOOR TILES The diagram
represents the floor tiles in
Michelle’s house. If m2 = 125,
find m3.
2  3
m2 = m3
125 = m3
Alternate Interior Angles Theorem
Definition of congruent angles
Substitution
Answer: m3 = 125
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
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10,
and m7 = x + 15, find x.
Explain your reasoning
5  7
m5 = m7
2x – 10 = x + 15
x – 10 = 15
x = 25
Answer: x = 25
Corresponding Angles Postulate
Definition of congruent angles
Substitution
Subtract x from each side.
Add 10 to each side.
Find Values of Variables
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
Substitution
Find Values of Variables
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
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
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
LESSON 3–2
Angles and Parallel Lines