DO NOW
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Take out a protractor
Take out your compass
Put your 2.6 Worksheet on
your desk ready to be
stamped.
In the picture to the left,
solve for x. Then find the
angle measures.
Announcements
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Test next Wednesday over angle relationships and
constructions.
Vocab and review (on website) are due
Wednesday.
Tutoring Tuesdays/Thursdays
Test corrections from Unit 1 are due next Friday.
Duplicating Segments and Angles, Constructing
Perpendicular Bisectors
Today’s Objectives
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Duplicate a line segment, an angle and a polygon
Construct perpendicular bisectors and midpoints
Make conjectures about perpendicular bisectors
Use Problem Solving skills
Creating Geometric Figures
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Sketch—Freehand, “looks like,” not accurate
Draw—Carefully use a straightedge and use
measurements from protractor, fairly accurate.
Construct—Don’t rely on protractor measurements.
Use compass and straightedge. Guaranteed to be
accurate.
Duplicating a Segment
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Step 1: Draw segment AB.
Step 2: Draw a ray starting at C.
Step 3: Open your compass to match the length of
AB.
Step 4: Put the point of your compass on point C
and drag the pencil to make an arc that intersects
the ray.
Step 5: Mark the intersection D.
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AB ≅ CD
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Duplicating an Angle
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Step 1: Draw ∠DEF.
Step 2: Draw a ray from point G.
Step 3: With your compass, put an arc around E that
intersects the rays ED and EF.
Step 4: Without changing the width of your compass,
put a matching arc around G.
Step 5: Open your compass to measure the distance
between intersection points in ∠DEF.
Step 6: Mark the same distance from the intersection
point in G through the arc.
Step 7: Draw a ray from G to the new intersection
point.
∠E ≅ ∠G
Practice
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Draw a segment that is 5cm (with ruler
measurements).
Construct a duplicate segment (without ruler
measurements, only using a compass and
straightedge).
Practice
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Draw an angle that is 70o (using a protractor)
Construct a duplicate angle (not using a protractor).
Perpendicular Bisectors—Terms
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A segment bisector—a line, ray, or segment that
passes through the midpoint of a segment.
 Cuts
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the line segment in half
Perpendicular lines—intersect at a right angle.
Perpendicular bisector—passes through the
midpoint of a segment at a right angle.
Equidistant—the same distance
Constructing Perpendicular Bisectors
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Step 1: Draw a line segment. Set your compass to
more than half the distance between the two
endpoints.
Step 2: Using one endpoint as center, swing an arc
on both sides of the segment.
Step 3: Using the same compass setting, swing an
arc from the other endpoint to intersect each arc.
Step 4: Mark your two intersection points and
connect them.
Perpendicular Bisector Conjecture
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If a point is on the perpendicular bisector of a
segment, then it is _________ from the endpoints.
equidistant
Converse of Perpendicular Bisector
Conjecture
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If a point is equidistant from the endpoints of a
segment, then it is on the _______________of the
segment.
perpendicular bisector
Also true!
Practice
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Draw and label AB. Construct the perpendicular
bisector of AB.
Practice
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Draw and label QD. Construct perpendicular
bisectors to divide QD into four congruent segments.
Stations!
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Direct: Practice Constructions
Collaborative: Without writing on the worksheets,
complete 3.1 and 3.2 worksheets on a separate
sheet of paper as a group. (Each person turn in
your own paper.)
Independent: Take your test and your notebook and
begin test corrections. If you are satisfied with your
test score, begin vocabulary that is due on
Wednesday.
Practice
Today’s Objectives
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Duplicate a line segment, an angle and a polygon
Construct perpendicular bisectors and midpoints
Make conjectures about perpendicular bisectors
Use Problem Solving skills
Exit Slip
For all exercises, do not erase your construction marks.
1.
Draw an obtuse angle. Label it ∠LGE, then
duplicate it.
2.
Draw a line segment. Label it RS, then duplicate it.
3.
Draw a line segment. Label it PQ, then construct its
perpendicular bisector.
4.
Draw two acute angles. Construct a third angle with
measure equal to the sum of the measures of the
first two angles. You may not use a protractor.
Exit Slip Honors
For all exercises, do not erase your construction marks.
1.
Draw an obtuse angle. Label it ∠LGE, then
duplicate it.
2.
Draw a line segment. Label it PQ, then construct its
perpendicular bisector.
3.
Draw two acute angles. Construct a third angle with
measure equal to the sum of the measures of the
first two angles. You may not use a protractor.
4.
Draw a quadrilateral QUAD. Duplicate it, matching
all the angles AND segments. Label the construction
COPY so that QUAD ≅ COPY.