### DO NOW

```DO NOW
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Take out a protractor
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
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
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
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.