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Inscribed AnglesActivities
(MCC9‐12.G.C.2; MCC9‐12.G.C.3)
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An angle inscribedin a semicircle
is a right angle.
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1. Construct a large circle.2. Construct a diameter. Label it AB.3. Inscribe 2 angles in the same semicircle.
Make sure the sides of each angle pass through A and B.
4. Measure each angle. What do you notice? A B
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Opposite angles ofa quadrilateral inscribed
in a circle areSupplementary.
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1. Construct a circle.2. Select four points on the circle.3. Construct a quadrilateral by connecting
those points.4. Measure each of the inscribed angles.5. Compare the measures.
What do you notice? 1
2
4
3
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Angles that interceptthe same arc are ≅.
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• Construct a circle.• Select 2 points on the circle. Label them A and
B.• Select a point P on the major arc. Construct
the inscribed angle ∠APB.• Measure ∠APB with your protractor. Record
the measure.A
BP
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• Select another point Q on the major arc. Construct the inscribed angle ∠AQB.
• Measure ∠AQB with your protractor. Record the measure.
• What do you notice? A
BP
Q
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The measure ofan angle with a vertex
on the circle is ½ ofcentral angle’s measure.
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1) Draw a circle.
2) Draw a central angle.
3) Measure of your central angle.
4) What is the relationship between
the central angle and its intercepted
arc?
The two measurements will be
equal.
5) Using the endpoints of the intercepted arc,
draw two chords that intersect at a point on the
circle but not on the intercepted arc.© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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7) Make a prediction about the measure of the
inscribed angle.
8) Measure the inscribed angle.
It should be ½ the measure of the central
angle.
9) Write a comparison about your predicted and
actual measurements of the two angles.
10) Compare your data with your partner.
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An angle with a vertexinside the circle has
a measure ½ of the sumof the intercepted arcs.
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1. Explain why m∠1 = m∠2 + m∠3.
2. What do we know about m∠DCE and m∠ACB?
C
DE
A B
∠1
∠2∠3
Exterior AngleTheorem
They are ≅. (Vertical ∠s)© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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1. Draw a circle.2. Choose point C in the interior of the
circle.
3. Draw 2 chords that intersect at C.4. Label A, B, D, E, and ∠1 as shown.
C
DE
A B
∠1
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5. Draw AD and label ∠2 and ∠3.
C
DE
A B
∠1
∠2∠3
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3. Write an equation for the m∠2.
4. Write anequationfor the m∠3.
5. Write an equation for the m∠1.
C
DE
A B
∠1
∠2∠3
m∠2 = (ED) ½
(
m∠3 = (AB) ½
(m∠1 = (ED) + (AB) ½ ½= (ED + AB) ½
( (
( (
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia