1. Parallel Lines and Transversals
LESSON 3–1
Parallel Lines and Transversals

2. Five-Minute Check (over Chapter 2) TEKS Then/Now New Vocabulary
Key Concepts: Parallel and Skew
Example 1: Real-World Example: Identify Parallel and Skew Relationships
Key Concepts: Transversal Angle Pair Relationships
Example 2: Classify Angle Pair Relationships
Example 3: Identify Transversals and Classify Angle Pairs
Lesson Menu

3. Make a conjecture about the next number in the sequence, 5, 20, 80, 320.
D. 1580
5-Minute Check 1

4. B. If you live in Massachusetts, then you do not live in Boston.
Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts.
A. If you do not live in Massachusetts, then you do not live in Boston.
B. If you live in Massachusetts, then you do not live in Boston.
C. If you do not live in Massachusetts, then you live in Boston.
D. You might live in Massachusetts or Boston.
5-Minute Check 2

5. A. Yes, A and B are a linear pair. B. no conclusion
Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements. If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles.
A. Yes, A and B are a linear pair.
B. no conclusion
5-Minute Check 3

6. A. Substitution Property B. Reflexive Property
Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.
A. Substitution Property
B. Reflexive Property
C. Addition Property
D. Symmetric Property
5-Minute Check 4

7. Find m1 and m2 if m1 = 8x + 18 and m2 = 16x – 6 and m1 and m2 are supplementary.
A. m1 = 106, m2 = 74
B. m1 = 74, m2 = 106
C. m1 = 56, m2 = 124
D. m1 = 14, m2 = 166
5-Minute Check 5

8. The measures of two complementary angles are x + 54 and 2x
The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle?
A. 24
B. 42
C. 68
D. 84
5-Minute Check 6

9. Mathematical Processes G.1(E), G.1(F)
Targeted TEKS
G.5(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a
variety of tools.
Mathematical Processes
G.1(E), G.1(F)
TEKS

10. You used angle and line segment relationships to prove theorems.
Identify relationships between two lines or two planes.
Name angle pairs formed by parallel lines and transversals.
Then/Now

11. consecutive interior angles alternate interior angles
parallel lines
skew lines
parallel planes
transversal
interior angles
exterior angles
consecutive interior angles
alternate interior angles
alternate exterior angles
corresponding angles
Vocabulary

12. Concept

13. A. Name all segments parallel to BC.
Identify Parallel and Skew Relationships
A. Name all segments parallel to BC.
Answer: AD, EH, FG
Example 1

14. B. Name a segment skew to EH.
Identify Parallel and Skew Relationships
B. Name a segment skew to EH.
Answer: AB, CD, BG, or CF
Example 1

15. C. Name a plane parallel to plane ABG.
Identify Parallel and Skew Relationships
C. Name a plane parallel to plane ABG.
Answer: plane CDE
Example 1

16. A. Name a plane that is parallel to plane RST.
A. plane WTZ
B. plane SYZ
C. plane WXY
D. plane QRX
Example 1a

17. B. Name a segment that intersects YZ.
A. XY
B. WX
C. QW
D. RS
Example 1b

18. C. Name a segment that is parallel to RX.
A. ZW
B. TZ
C. QR
D. ST
Example 1c

19. Concept

20. Answer: corresponding
Classify Angle Pair Relationships
A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: corresponding
Example 2

21. Answer: alternate exterior
Classify Angle Pair Relationships
B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate exterior
Example 2

22. Answer: consecutive interior
Classify Angle Pair Relationships
C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: consecutive interior
Example 2

23. Answer: alternate interior
Classify Angle Pair Relationships
D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate interior
Example 2

24. A. Classify the relationship between 4 and 5.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 2a

25. B. Classify the relationship between 7 and 9.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 2b

26. C. Classify the relationship between 4 and 7.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 2c

27. D. Classify the relationship between 2 and 11.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Example 2d

28. Identify Transversals and Classify Angle Pairs
A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.
Example 3

29. Identify Transversals and Classify Angle Pairs
B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.
Example 3

30. Identify Transversals and Classify Angle Pairs
C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles.
Example 3

31. A. HIKING A group of nature trails is shown
A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal.
A. lines c, f
B. lines c, d, e
C. lines c, d, f
D. lines c, d, e, f
Example 3a

32. B. HIKING A group of nature trails is shown
B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal.
A. no lines
B. lines c, f
C. lines c, d, e, f
D. lines a, c, d, e, f
Example 3b

33. C. HIKING A group of nature trails is shown
C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal.
A. no lines
B. lines a, b, d, e, f
C. lines a, d, f
D. lines a, b, e
Example 3c

34. Parallel Lines and Transversals
LESSON 3–1
Parallel Lines and Transversals