Construct Parallel Lines
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Printed: July 20, 2012
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C ONCEPT
1
1
Construct Parallel Lines
Lesson Plan
Launch (10 min)
• Students: State the measurements of the 7 other angles in the diagram, giving a reason for each statement.
– Watch out for students connecting a new angle measurement to another angle that has yet to have been
figured out. The logical break here should be pointed out.
– Make sure students use each ‘reason’ once.
Presentation (25 min)
• (5 min) Intro : Have the students decide whether each picture is parallel and state why. Come to the conclusion:
If we have congruent corresponding angles, then we have parallel lines.
• (10 min) Teacher Demo : Lead students through a construction of a line parallel to a given line passing through
a given point. Students then try the same process on their own.
– Highlight the corresponding angles to show that they are congruent
– Highlight the mini-arcs to emphasize their importance as evidence of the construction (don’t erase!)
• (15 min) Students apply this process of creating parallel lines by creating congruent angles (angle copy) to a
city planning exercise.
Practice (15 min)
• Train Your Coworker: Students pair up. One remains silent and uses a straightedge and compass to construct a
line parallel to a given line through a given point. They do only what their partner tells them to do and cannot
ask questions. Emphasize being specific!
• Parallel?: Students determine if there is enough evidence to know that the lines are parallel. Make sure to
connect back to the new big idea: that the converse of our theorem is true, if we have congruent corresponding/alt.int./alt.ext. angles or supplementary consec. int. angles, then we must have parallel lines.
• What Do We Need: Students figure out what the value of the unknown needs to be in order to make the lines
parallel.
Conclusion (10 min)
• Sequence steps to construct a line parallel to given line through a given point. Pair share. Share out.
Exit Ticket (5 min)
∗ Most
Common Mistakes:
• Students erase their mini-arcs and other evidence of their construction. Don’t erase the evidence!
Concept 1. Construct Parallel Lines
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∗ Best
Practices:
• Highlighting mini-arcs can really help the students remember to preserve them for evidence
• Doing reciprocal teaching, having one student tell another what to do while the person constructing cannot
speak helps students refine the construction process in their heads
• Connecting the constructing to city streets places this skill in a real-world context, giving it greater meaning
and helping it make sense for the students more.
Launch
Angle Pairs: Find Their Measurements & Give Reasons Why
Given: Lines l and m are parallel; measure of angle 1 = 110◦
Find the measure of the other angles, giving a reason for each of their measures.
Note: You may only use each reason from the bank below once .
Supplementary
Corresponding Angles
Linear Pair
Same-Side Interior Angles
The m6 1 is 110◦
Alternate Interior Angles
because it is given.
The m6 2 is
because 6 2 and 6 1 are
The m6 3 is
because 6 3 and 6
m6
4 is
because
The m6 5 is
because
The m6 6 is
because
The m6 7 is
because
The m6 8 is
because
The
Presentation
Part 1: Construction
are
Alternate Exterior Angles
Vertical Angles
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Are the lines parallel? Why/ why not?
_____________________________________________________________
_____________________________________________________________
Are the lines parallel? Why/ why not?
_____________________________________________________________
_____________________________________________________________
Conclusion:
_____________________________________________________________
So, if we create congruent corresponding angles then we create parallel lines . Pretty cool if our goal is to create
some parallel lines. Let’s see how this could work.
Part 2: City Planning
Ex. 1: Kaiser Hospital
You work for the city planning department of Hayward. Kaiser Hospital wants 2 new driveways built. Your boss
wants you to create a plan for those driveways.
a. Extend Loyola Avenue northwest into the hospital through point A towards Tennyson Avenue
b. Create another road parallel to Bolero Avenue that passes through point A.
Your boss insists on you using your compass and straightedge to construct your plan instead of a ruler and protractor.
Why do you think that is?
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Ex. 2: Mt. Eden Park
Your next task is to add 2 walking paths to Mt. Eden Park.
a. Create a new walking path from Point Q through and past Point P up to the road.
b. Create a second path that is parallel to West Tennyson Rd and passes through point P.
Practice
Part 1 – Train Your Coworker
You must train your coworker to construct parallel lines. Your coworker has the compass and straightedge and cannot
talk. Tell them what to do step-by-step to create a parallel line through point P and parallel to line k. Be sure to be
specific as they cannot ask you any questions!
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Part 2 – Parallel?
Big Idea: We learned that if we create congruent corresponding, alternate interior or alternate exterior angles (or
supplementary consecutive interior angles), then we have created parallel lines.
Is there enough information to prove c || d? Write YES if there is and NO if not. If YES, state the reason.
1.
2.
3.
4.
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Part 3 – What Do We Need?
Figure out what the unknown needs to be in order for the lines to be parallel. Remember the big idea above.
What value for x will make lines a and b parallel?
5.
6.
Describe the next step in the construction:
7.
Conclusion
The following steps describe how to construct a line parallel to a given line through a given point. They are out of
order. Put the steps in order by correctly numbering the boxes from left to right. Sketch a picture of the construction
at each stage.
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Homework
Is there enough information to prove c || d? Write YES if there is and NO if not. If YES, state the reason.
1.
2.
3.
4.
Concept 1. Construct Parallel Lines
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What value for x will make lines a and b parallel?
5.
6.
Describe the next step in the construction:
7.
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Exit Ticket
Concept 1. Construct Parallel Lines