I. Construct Circle P
(Label the child). Construct a point on the circle, label as point
Choose point T and center P;
construct "line". Choose this line and the circle; construct
"point at intersection"; label as K.
Construct segment TK, hide line
TK. TK should be a diameter.
Construct a point on the circle;
label as A.
Choose point A and segment TK;
construct "perpendicular line".
Choose this line and the circle;
construct "point at intersection"; label as B.
Construct segment AB; hide line
Choose segment TK and segment
AB; construct "point at intersection"; label as R.
Construct segments AP and PB.
(Make sure that point K is between the minor arc AB).
PRA = , therefore Triangle PRA is a triangle.
Using the Pythagorean Theorem,
show that your conjecture about Triangle PRA is true.
PA = PB = PK =
All three segments are
PR = RK =
What is the relationship between
these two segments and PK?
AB = AR = RB =
Arc AB = Arc AK = Arc KB =
In a circle, if a diameter is
perpendicular to a chord, then it the chord and its arc.
Construct Circle C. Choose
the circle and "measure" radius.
Move the circle using the child
until the radius is equal to 4 cm.
Construct two chords (non-intersecting),
label as PQ and RS.
Let PQ = 5 and RS = 5.
Arc PQ = Arc RS =
In circle, two minor arcs are
if and only if their
corresponding chords are congruent.
Construct the midpoints of segments
PQ and RS. Label as M and N, respectively.
Construct the perpendicular bisector
of segment PQ and RS. (Choose the midpoint and the segment, construct
What can you conclude about the
perpendicular bisectors of chords of a circle?
Construct segment MC; hide line
Construct segment NC; hide line
MC = NC = PQ =
In a circle, two chords are if and only if they are from the center.
Make PQ and RS equal to 5, then
6, then 7. Does your conjecture hold true?
Define Inscribed Angle:
Construct Circle B. Construct
three points on the circle, label as X, Y, and Z.
(Make sure Y is between points
X and Z).
Construct chords XY and YZ.
Measure XYZ and move chords around
until the angle is 65 degrees.
Measure Arc XZ = This is called the "intercepted arc".
If an angle is inscribed in a
circle, then what can you conclude about the intercepted arc?
Make XYZ equal to 90 degrees.
What can you conclude about its intercepted arc?
This arc is known as .
Make XYZ equal to 40 degrees.
Construct a point, W in between points X and Y on the circle.
Construct segments WX and WZ.
XWZ = The intercepted
arc for this angle is Arc
and equals .
It two inscribed angles of a
circle intercept the same arc, then the angles are .
Construct Circle A. Construct
four points on the circle, P, Q, R, and S.
Construct segments PQ, QR, RS,
and PS. This is called an "inscribed polygon".
Define Inscribed Polygon:
QPS = QRS = PQR =
If a quadrilateral is inscribed
in a circle, then its opposite angles are .
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