Ch 4.3
Transversals & Corresponding Angles
Ch 4.3
Transversals and
Corresponding Angles
Learning Target:
I will be able to use theorems to determine the
relationships between specific pairs of angles
and to use algebra to find angle
measurements
Standard 7.0
Students prove and use theorems involving the
properties of parallel lines cut by a transversal.
Ch 4.3
Postulate 4-1
Transversals & Corresponding Angles
Ch 4.3
Transversals & Corresponding Angles
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
Ch 4.3
Transversals & Corresponding Angles
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
Ch 4.3
Transversals & Corresponding Angles
Classwork #1
A. In the figure, a || b and
m18 = 42. Find m22.
A. 42
B. 84
C. 48
D. 138
Ch 4.3
Transversals & Corresponding Angles
Classwork #1
B. In the figure, a || b and
m18 = 42. Find m25.
A. 42
B. 84
C. 48
D. 138
Ch 4.3
4-1
4-2
4-3
Transversals & Corresponding Angles
Ch 4.3
Transversals & Corresponding Angles
Ch 4.3
Transversals & Corresponding Angles
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
Ch 4.3
Transversals & Corresponding Angles
Classwork #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
Ch 4.3
Transversals & Corresponding Angles
Find Values of Variables
A. ALGEBRA If m5 = 2x – 10,
and m7 = x + 15, find x.
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.
Ch 4.3
Transversals & Corresponding Angles
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
m6 + m4= 180
Substitution
Supplement Theorem
4y + 4(y – 25) = 180
Substitution
4y + 4y – 100 = 180
Distributive Property
8y = 280
y = 35
Property.
Additive Inverse Property.
Multiplicative Inverse
Ch 4.3
Transversals & Corresponding Angles
Classwork #3
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
Ch 4.3
Transversals & Corresponding Angles
Classwork #3
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
Ch 4.3
Theorem 4-4
Transversals & Corresponding Angles