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Name: ____________________________ Period: ________ 3.1 Parallel Lines and Transversals
PARALLEL LINES AND TRANSVERSALs
In this investigation you need a protractor and a ruler (or other straight edge).
Lay your ruler in the space below. Trace along both sides of the ruler so you will have a set of parallel lines.
Then draw a third line that crosses the two parallel lines, this is the transversal. Do not make right angles.
Label all 8 angles starting with 1, 2, 3 and so on. Measure each angle and record its degree measurement in the table.
Angle (^) 1 2 3 4 5 6 7 8 Measurement
Observe which angle pairs are congruent. Choose a color pencil/crayon and color each set of angles which are congruent the same color. How many colors did you use?
What do you observe about the pairs of angles that are colored differently?
Questions 1-6: Label each angle pair by their relationship “vertical, alternate interior, alternate exterior, corresponding.” Solve for x, show your work.
Question 7 – 10
Decide whether each statement is TRUE or FALSE. If the statement is false, correct the statement.
_____ m || n line m
_____ ∠1 and ∠5 are vertical angles
_____ ∠2 and ∠8 alternate exterior
_____ ∠3 and ∠5 are same side interior line n
For the given information, tell which pair of the lines (if any) above must be parallel. State the relationship that supports your answer.
Which lines? Support?
Example: ∠ 1 ≅ ∠ 9 line m || n If alternate exterior angles are ≅ then lines ||
Name: _________________________ Period: ________ 3.3 Sidewalk Lab
Part 1. Your group has been asked to determine the quality of the layout of the concrete sections of sidewalk poured at Tanque Verde High School. The breaks in the concrete should be parallel lines. Your group should prove those sections are indeed parallel.
With your group, find a section of sidewalk that contains at least three adjacent rectangular sections.
Using appropriate tools, draw a CHALK transversal through all three sections. Record on diagram.
Measure at least three angles. Record on diagram below.
Measure the outside edge of all six lengths of the sidewalk. Record on diagram
Measure this width Measure this width Measure this width Check list:
□ These three rectangles represent sections of sidewalk
□ Draw your transversal (chalk line)
□ Label the diagram with your angle measurements
□ Label your 6 segment widths
Measure this width Measure this width Measure this width Measure this width Measure this width Measure this width
Classify an angle pair that your group measured _______________________________________ What relationship do those angles have that proves that the line segments are parallel? You should write a conditional statement that starts with “If ------- are ----- then lines are parallel”
How are the outside widths of the cement blocks related? How do those measurements prove that the line segments are parallel?
Name: _________________________ Period: ________ 3.4 Angle Puzzles
- Find all the angle measurements, show your calculations:
a = _____
b= _____
c= _____
d= _____
e= _____
f= _____
- What is wrong with each diagram? Explain.
a) 𝐴𝐵 ⃡ ⊥ 𝐶𝐷⃡ B c) F M
370 L
C 390
460 E G 420 D H
A
b) 1200 600
1200
- How many angles must you be given to find all the other angle measurements? Which one(s)?
a= _____
b= _____
c= _____
d= _____
e= _____
f= _____
g= _____
h= _____
k= _____
m= _____
n= _____
p= _____
q= _____
r= _____
s= _____
All of Ms. Jones’ children were born in June. Their birthdays are June 1, June 7, June 12, June 20 and
June 29. There are three girls named Mary, Elvira and Joan and there are two boys named Douglas
and Timothy. Ms. Jones bought these five presents for them: a book, a coat, concert tickets, a dress,
and an electronic game. From the information given, determine the birthday and present received by
each child.
1) Timothy’s birthday comes before that of the girl who received a dress but after the girl who
received a coat.
2) Douglas’s birthday comes before Elvira’s birthday but after the birthday of the girl who received an
electronic game.
3) Elvira did not receive the dress and neither did Joan
4) Douglas did not get the book as a present.
Birthday Gift
Douglas
Elvira
Joan
Mary
Timothy
Name: __________________________________ Period______ 3.6 Review for Quiz: Parallel Lines, Transversals and Parallelism
- Lines m || n || p. Use the figure to identify the type of angle pairs indicated.
a) ______________________________ b) ______________________________
c) ______________________________ d) ______________________________
- Find the indicated angle measures
__________________________ __________________________ _________________________
- Solve for x 4) Find the value of x, y and z.
