Constructions, Copy and Bisect
Segments
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Printed: July 20, 2012
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C ONCEPT
1
1
Constructions, Copy and
Bisect Segments
Lesson Plan
Launch (10 min)
• Students : Sketch a circle by hand and another using a compass. They will notice how the compass will give
them a more perfect circle if used correctly.
• Have the answers to last night’s homework with work shown on the board when students walk in class. Once
students finish their launch, have them check their answers from the answers on the board. Before debriefing
launch, go over difficult problems from last night’s HW and ask for specific questions.
• Debrief : Allow students an opportunity to share their experience to #3 and #4. If you have a document
camera, show some student work of hand drawn circles and using the compass.
Presentation (35-40 min)
• (10 min) Vocabulary : Define each word (under the word) then sketch a picture of each (to the right of the
word)
• (10 min) Copy a Segment : Project the instructions on the board but reveal them to the students one by one.
Have a student read each step aloud then, with the class, copy segment AB in the notes. After each step, have
the students write their own version of the same instructions (remind them of yesterdays conclusion and to
make it a clear sentence that anyone could understand). Once you’ve went through this once together, have
the students try again, on their own, following their own instructions silently. Repeat if necessary.
• (10 min) Perpendicular Bisector : Remind the students what it means to be a “Perpendicular Bisector” but
breaking down each word individually. Repeat the same process as “Copy a Segment” to complete this
construction.
• (optional10 min, If you feel you have enough time) Reciprocal Teaching : Have the students turn to a neighbor.
Student #1 reads their instructions exactly to Partner #2 for “Copy”. Once Done, Student #2 offers feedback
on what would make their instructions better. Then partners switch. If time, encourage them to do the same
for “Perp. Bisect.”
Practice (10-15 min)
• Practice is Higher Level in this lesson. Allow the students to struggle with it and encourage them to think
outside the box.
Exit Ticket (5 min)
Materials
• Instructions for “Copy a Segment” and “Perpendicular Bisector”
Concept 1. Constructions, Copy and Bisect Segments
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• Class Set Compasses, Straightedge
• Lesson Packets
Copy a Segment: (Given; Segment AB)
Step 1: Use a straightedge to draw a segment longer than AB. Label point C on the new segment.
Step 2: Place the needle of your compass on A. Set your compass at the length of AB.
Step 3: Without changing the compass, place the needle of your compass on C. Draw an Arc. Mark this point D.
Perpendicular Bisector: (Given: Segment AB)
Step 1: Place the needle of the compass at A. Use a compass setting that is greater than half the length of AB. Draw
a large arc.
Step 2: Without changing the compass, place the needle at B. Draw a large arc. It should intersect the other arc at
two points.
Step 3: Using a straightedge, draw a segment through the two points of the intersection. Label the intersection with
AB, point M.
Launch
1. Sketch the best circle you can using only your pencil.
2. Draw the best circle you can using any of the tools on your desk.
3. Architects use these tools to draw floor plans and construction plans for buildings. Why do you think they use
them instead of just drawing it by hand?
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Presentation
Vocabulary
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TABLE 1.1:
Practice “Copy a Segment” construction
Instructions
Copy a segment
Given : Segment AB
Step 1 : Use a straightedge to draw a segment longer
than AB. Label point C on the new segment.
Step 2 : Place the needle of your compass on A. Set
your compass at the length of AB.
Step 3 : Without changing the compass, place the
needle of your compass on C. Draw an Arc. Mark
this point D.
Conclusion:
• Segment AB is congruent to segment CD.
Practice “Perpendicular Bisector” construction
Written instructions
Concept 1. Constructions, Copy and Bisect Segments
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TABLE 1.1: (continued)
Practice “Copy a Segment” construction
Instructions
Perpendicular Bisector
Given : Segment AB
Step 1 : Place the needle of the compass at A. Use
a compass setting that is greater than half the length
of AB. Draw a large arc.
Step 2 : Without changing the compass, place the
needle at B. Draw a large arc. It should intersect the
other arc at two points.
Step 3 : Using a straightedge, draw a segment
through the two points of the intersection. Label the
intersection with AB, point M.
Conclusion:
• Point M is bisects line AB.
• The line is perpendicular to AB.
Practice
1. Copy the segment below. (refer to your notes if you need to)
2. Construct a perpendicular Bisector.
3. How many bisectors can a line segment have? Explain.
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4. Can you bisect a line ? Why or why not?
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5. Use a compass and a straightedge to draw a segment that is twice as long as AN.
Explain how you did this below...
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6. CHALLENGE : Using “Copy a Segment” and “Perpendicular Bisector” constructions, construct a square below.
(Extension: Explain how you completed this construction)
Homework
1. What is the first step to “Copying a Segment?”
2. Segment DF is 22 inches in length. After constructing a perpendicular bisector, what is the length from point D
to the point made by the construction?
3. Below are the steps to Construct a Perpendicular Bisector except they are out of order.
Concept 1. Constructions, Copy and Bisect Segments
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I. Without changing the compass, place the needle at B. Draw a large arc. It should intersect the other arc at two
points.
II. Using a straightedge, draw a segment through the two points of the intersection. Label the intersection with AB,
point M.
III. Place the needle of the compass at A. Use a compass setting that is greater than half the length of AB. Draw a
large arc.
Rearrange the steps in the correct order
4. Below are the steps to Construct a Segment Copy except they are out of order.
I. Without changing the compass, place the needle of your compass on C. Draw an Arc. Mark this point D.
II. Place the needle of your compass on A. Set your compass at the length of AB.
III. Use a straightedge to draw a segment longer than AB. Label point C on the new segment.
Rearrange the steps in the correct order
5. Solve for x given Point S is between Point R and Point T . (hint: sketch a picture)
RS = 2x, ST = 3x, RT = 25
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Exit Ticket
Concept 1. Constructions, Copy and Bisect Segments