© 2009, dr. jennifer l. bell, lagrange high school, lagrange, georgia

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