Download Constructing Perpendicular Bisectors

7F
Constructing Perpendicular Bisectors
You will need
•
•
•
•
a ruler
paper for folding
a protractor
a transparent
mirror
• a compass
GOAL Investigate methods of constructing a perpendicular bisector of a segment.
Explore the Math
Chang is exploring methods of constructing a perpendicular bisector.
? How can you construct a perpendicular bisector?
A. Draw segment EF. Fold the paper so that half the segment is exactly over the
other half. Unfold the paper. Draw a line along the fold.
B. Measure segment EF and each segment created. Mark the equal lengths. Predict
the measure of each angle created. Check your prediction. Mark the right angles.
C. Draw segment LM. Use a transparent mirror to construct the line of symmetry.
Why is the line of symmetry the perpendicular bisector of segment LM?
perpendicular
bisector
a line that divides
a segment into
two congruent
segments and
meets or crosses
the segment at
right angles
D. Mark the equal lengths and right angles.
E. Draw segment ST. Adjust a compass so that the
distance between the pencil tip and compass point
is greater than half the length of segment ST. With
the compass point on point S, draw arcs above
and below segment ST.
F. Keep the distance between the pencil tip and compass
point the same as in step E. With the compass point
on point T, draw arcs above and below segment ST to
intersect with the other arcs.
C
S
T
A
B
D
S
CD is the
perpendicular
bisector of AB.
Equal segments
are marked
with the same
number of tick
marks. Right
angles are
marked as
square corners.
T
G. Join the points where the arcs intersect. Mark the equal
lengths and right angles.
Reflecting
1. In step E, why is it necessary to make the distance between the
pencil tip and compass point greater than half the length of segment ST?
2. How is a perpendicular bisector of a segment the same as a line of symmetry?
3. The measure of a straight angle along a segment is 180º. Why is each angle formed
by a perpendicular bisector a right angle?
4. How do your constructions show the meaning of a perpendicular bisector?
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Chapter 7: 2-D Geometry
Copyright © 2006 by Thomson Nelson