Chords
Jenni McIntire and Teresa Davis
This lab is to explore properties of chords of a circle.
A chord is a segment whose endpoints are on
the circle.
Investigation:
In Sketchpad, make the
following construction.
- Construct circle A with chord CD
- Find the midpoint of CD and label this point M.
- Construct a radius through M.
- Measure angle AMC.
What do you notice about these measures? What conjecture can
you make about a raduis that bisects a chord? Do you think this
would work the opposite way?
Investigation:
In Sketchpad, make the
following construction.
- Construct circle A with chord CD.
- Construct point E on the circle.
- Construct a new circle with center E and radius CD.
- Choose either of the point of intersections of the two circles
and label this point F.
- Hide the second circle and construct the chord EF.
- You have constructed EF to be congruent to CD. Measure to
verify.
- Construct the radii AC, AD, AE, and AF.
- Measure the central angles CAD and EAF.
What do you notice about these measures? What conjecture can
you make about central angles formed by congruent chords? If you
move any of the points, does you conjecture remain true?
- Measure the minor arcs CD and EF(use arc angle).
What do you notice about these measures? What conjecture can
you make about arcs formed by congruent chords? If you move any
of the points, does you conjecture remain true?
Investigation:
In Sketchpad, make the
following construction.
- Construct a circle with a diameter.
- Measure the diameter and the circumference of the circle.
- Move the circle around to get 10 different measures. Click
here to enter these measures
in a spreadsheet. Circumference in the 1st column and diameter
in the 2nd.
The addition, subtraction, multiplication,and division of your
data is in columns 3, 4, 5, and 6 respectively. Do you notice
anything about these computations?
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