Angles and Parallel Lines LESSON 3–2. Lesson Menu Five-Minute Check (over Lesson 3–1) TEKS...
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Transcript of Angles and Parallel Lines LESSON 3–2. Lesson Menu Five-Minute Check (over Lesson 3–1) TEKS...
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Angles and Parallel Lines
LESSON 3–2
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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
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Over Lesson 3–1
A. RST
B. PON
C. STQ
D. POS
Choose the plane parallel to plane MNR.
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Over Lesson 3–1
A. PM
B. TS
C. PO
D. MQ___
___
___
___
Choose the segment skew to MP.
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Over Lesson 3–1
A. corresponding angles
B. vertical angles
C. consecutive interior angles
D. alternate exterior angles
Classify the relationship between 1 and 5.
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Over Lesson 3–1
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. consecutive interior angles
Classify the relationship between 3 and 8.
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Over Lesson 3–1
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. vertical angles
Classify the relationship between 4 and 6.
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Over Lesson 3–1
A. OS
B. TS
C. NR
D. MQ
Which of the following segmentsis not parallel to PT?
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Targeted TEKSG.6(A) Verify theorems about angles formed by theintersection of lines and line segments, includingvertical 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 ProcessesG.1(A), G.1(G)
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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.
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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
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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
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A. 42
B. 84
C. 48
D. 138
A. In the figure, a || b and m18 = 42. Find m22.
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A. 42
B. 84
C. 48
D. 138
B. In the figure, a || b and m18 = 42. Find m25.
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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
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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.
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A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Explain your reasoning
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
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B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Find Values of Variables
8 6 Corresponding AnglesPostulate
m8 = m6 Definition of congruentangles
4y = m6 Substitution
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Find Values of Variables
m6 + m4 = 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
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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
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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
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Angles and Parallel Lines
LESSON 3–2