Arcs and Angles of Circles
Jenni McIntire and Teresa Davis
This lab is to explore central angles and inscribed angles
and there intercepted arcs.
A central angle is an angle formed by two radii.
A central
angle's vertex is on the center of the circle.
An inscribed angle is an angle whose vertex
is on the
circle and whose sides intercept the circle.
Investigation:
In Sketchpad, make the
following construction.
- Construct circle A.
- Construct points C and D on the circle and construct the
radii AC and AD.
- Construct point E on the circle and move it so that it is
on the exterior of the central angle CAD.
- Construct the chords CE and CE to create the inscribed angle
CED
- Measure the central angle and the inscribed angle and the
minor arc CD (arc CD is called the intercepted arc).
What is the relationship between the central angle and its
inercepted arc? Move point C or D to see the relationship between
the inscribed angle and its intercepted arc. What conjectures
can you make
Investigation:
In Sketchpad, make the
following construction.
- Construct circle A with diameter BC.
- Construct a point D on the circle and chords BD and CD.
- Measure the angle BDC.
Move point D around the circle. What do you notice about the
measure of the angle? Can you explain why this is so?
Investigation:
In Sketchpad, make the
following construction.
Construct circle A.
Construct secant CD where C and D are on the circle.
Construct point E on the circle and a line through E parallel
to CD.
Construct the point of intersection of the new line and the
circle and label it F.
Measure the arcs detween the parallel lines.
What do you notice about these measures? What conjecture can
you make about the arcs between parallel lines? Move the points
around, does your conjectur always remain true?
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