ch 4.3 transversals and corresponding angles ch 4.3 standard 7.0 students prove and use theorems...
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Ch 4.3Transversals and
Corresponding Angles
Ch 4.3
Standard 7.0Students prove and use theorems involving the properties of parallel lines cut by a transversal.
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
Transversals & Corresponding Angles
Ch 4.3 Transversals & Corresponding Angles
Postulate 4-1
Use Corresponding Angles Postulate
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
Answer: m15 = 51
15 11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
Ch 4.3 Transversals & Corresponding Angles
Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
Answer: m16 = 51
16 15 Vertical Angles Theorem
15 11 Corresponding AnglesPostulate
16 11 Transitive Property ()
m16 = m11 Definition of congruent angles
m16 = 51 Substitution
Ch 4.3 Transversals & Corresponding Angles
A. 42
B. 84
C. 48
D. 138
A. In the figure, a || b and m18 = 42. Find m22.
Ch 4.3 Transversals & Corresponding Angles
Classwork #1
A. 42
B. 84
C. 48
D. 138
B. In the figure, a || b and m18 = 42. Find m25.
Ch 4.3 Transversals & Corresponding Angles
Classwork #1
Ch 4.3
4-1
4-2
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 m2 = 125, find m3.
2 3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125
Ch 4.3 Transversals & Corresponding Angles
A. 25
B. 55
C. 70
D. 125
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
Ch 4.3 Transversals & Corresponding Angles
Classwork #2
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables
5 7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x + 15 Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
Ch 4.3 Transversals & Corresponding Angles
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Find Values of Variables
8 6 Corresponding Angles Postulate
m8 = m6 Definition of congruent angles
4y = m6 Substitution
Ch 4.3 Transversals & Corresponding Angles
m6 + m4= 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Additive Inverse Property.
y = 35 Multiplicative Inverse Property.
A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 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 m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.
A. y = 14
B. y = 20
C. y = 16
D. y = 24
Ch 4.3 Transversals & Corresponding Angles
Classwork #3
Ch 4.3 Transversals & Corresponding Angles
Theorem 4-4