Download Investigation with Parallel Lines

Name: ___________________________________ Date: _____________
Transversals and Parallel Lines
SCORE: _______/25 pts
What does it Mean to be Parallel in both Geometry and Algebra?
In Geometry, for two lines to be parallel, what two criteria must they have?
In Algebra, for two lines to be parallel, what criteria must they have?
Let’s investigate this to determine the answer:
First – recall slope-intercept form:
𝑦 = 𝑚𝑥 + 𝑏
2
Equation of line: 𝑦 = 3 𝑥 + 5
Draw TWO more lines that are parallel
to the line given. Then determine the
equation of both lines.
The two lines that you drew, are they
parallel to each other? Why or why not?
(answer in complete sentences)
In complete sentences, describe how you know that the two lines that you drew and the given line meet the criteria for
Geometry. (May use the back if needed)
Name: ___________________________________ Date: _____________
Transversals and Parallel Lines
SCORE: _______/ 175 pts
Investagation of Angles with Parallel Lines
Part 1 – Following the four steps, complete the table, then answer the question(s): (10 pt)
Step 1: Construct a line (cannot be vertical nor horizontal) and label two points on the line A and B.
** Every group members first two lines must have different slopes.**
Step 2: Construct a line parallel to line AB. Label two points on this line C and D. (be sure to show lines are parallel
on diagram)
Step 3: Construct a transversal ⃡𝐸𝐹 , label the points of intersection G and H respectively.
Step 4: Use a protractor to measure each angle. (helpful hint – it might be easier if you make the lines extend really
far) Write the angle measures in the chart below: (20 pt)
Angle
Your
Measure
Group
Measure
Group
Measure
Group
Measure
∠𝐴𝐺𝐸
∠𝐵𝐺𝐸
∠𝐴𝐺𝐻
∠𝐵𝐺𝐻
∠𝐶𝐻𝐺
∠𝐷𝐻𝐺
∠𝐶𝐻𝐹
∠𝐷𝐻𝐹
Here is an example of what your graph should look like, remember your lines do not have to go in the same directions
as the example, but your points should be labeled the same way.
Investigate the following:
1. Identify all six angle relationships pairs in the diagram 1. Then determine what conjecture, if any, can be made able
their angle measures? (15 pt)
Part 2 – On a separate graph, repeat the first four steps again, HOWEVER, this time, make sure that line CD is NOT
PARALLEL to line AB. (30 pt)
Angle
Your
Measure
Group
Measure
Group
Measure
Group
Measure
∠𝐴𝐺𝐸
∠𝐵𝐺𝐸
∠𝐴𝐺𝐻
∠𝐵𝐺𝐻
∠𝐶𝐻𝐺
∠𝐷𝐻𝐺
∠𝐶𝐻𝐹
∠𝐷𝐻𝐹
2. Identify all six angle relationships pairs in the diagram 2. Then determine what conjecture, if any, can be made able
their angle measures? (15 pt)
3. Compare and Contrast the two diagrams. What happens with the angles relationships when lines are parallel vs.
when lines are not parallel? What is the same in both situations? Why do you think this is true? Write your answers in
a well-thought out paragraph, making sure you answer all questions clearly and correctly. (20 pt)
APPLY WHAT YOU’VE LEARNED
The blueprint contains many examples of the types of angle pairs you learned about this week and during this
investigation, some formed by parallel lines and a transversal, and some formed by nonparallel lines and a transversal.
Find the measure of ALL numbered angles in the blueprint. (2 pt)
Record your measures in the table below:
∠1 =
∠2 =
∠3 =
∠4 =
∠5 =
∠6 =
∠7 =
∠8 =
∠9 =
∠10 =
∠11 =
∠12 =
∠13 =
∠14 =
∠15 =
∠16 =
∠17 =
∠18 =
∠19 =
∠20 =
∠21 =
∠22 =
∠23 =
∠24 =
∠25 =
∠26 =
∠27 =
∠28 =
∠29 =
∠30 =
∠31 =
∠32 =