© 2009, dr. jennifer l. bell, lagrange high school, lagrange, georgia
TRANSCRIPT
Inscribed AnglesActivities
(MCC9‐12.G.C.2; MCC9‐12.G.C.3)
An angle inscribedin a semicircle
is a right angle.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Opposite angles ofa quadrilateral inscribed
in a circle areSupplementary.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
Angles that interceptthe same arc are ≅.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
• 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
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
• 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
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
The measure ofan angle with a vertex
on the circle is ½ ofcentral angle’s measure.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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
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.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
An angle with a vertexinside the circle has
a measure ½ of the sumof the intercepted arcs.
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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
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
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
5. Draw AD and label ∠2 and ∠3.
C
DE
A B
∠1
∠2∠3
© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia
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