1. Have Out: U10D3 Bellwork: Complete the bellwork on your packet.
pencil, highlighter, red pen, calculator, HW, GP NB
Bellwork:
Complete the bellwork on your packet.
Here are some of the new justifications:
circle = 360°
arc measure = central 
arc length =
m AB
360 r
Asector = 

2. Determine the length of the following arcs:
1. AB
72 A O B
5 in +1
Length of
2. CD C
8 m
120 O D +1

3. Determine the area of the following:
Asector AOB = 72
360  5
3. Sector AOB +1
72 A O B
5 in = 1 5
 52 = 1 5
 25
= 5 in2 +1
 in2 +1 C
Asector COD =
120
360  8 +1
4. Sector COD
8 m
120 = 1 3
 82 O D = 1 3
 64 +1 +1
 m2

4. Vocabulary
Add to your notes
Inscribed Angle:
Angle with its vertex on the circle and whose sides intersect the circle.
Intercepted Arc:
Arc formed by the intersection of the two sides of the angle & the circle.
Now take out your CS 21 Resource page and 3 different colored writing utensils. You also need a piece of tracing paper.

5. Now try parts a – f. Add to your notes A Inscribed Angle Theorem:
CS-22
Add to your notes A D B
Inscribed Angle Theorem:
The measure of any inscribed angle is half the measure of its intercepted arc.
mADB = ½ mAB
Likewise, any intercepted arc is twice the measure of any inscribed angle whose sides pass through the endpoints of the arc.
mAB = 2mADB
Now try parts a – f.

6. Find the measure of the indicated angles & arcs. a) b) c) x 118 x c y
56
41 c y
(Inscribed  Thm)
(Inscribed  Thm)
x = ½118
x = 241
(Arc measure = central )
x = 59
x = 82
x = 56
(Inscribed  Thm)
y = ½x
y = ½56 z
y = 28
114
d) e) f)
78 x x y C
28 x y y

7. Find the measure of the indicated angles & arcs.z
114
d) e) f)
78 x x y A C
28 x y y
( Sum Thm.)
mA + 78 + 90 = 180
(Inscribed  Thm.)
mA = 12
(Arc measure = central )
x = 228
(Inscribed  Thm)
x= 114
x = 56
z = 212
(Inscribed  Thm.)
(Inscribed  Thm.)
z = 24
y = ½114
y = ½x
(Inscribed  Thm)
y = 57
y = ½56
x = 290
x = 180
y = 28
(Inscribed  Thm)
y = 278
y = 156

8. Arc formed by the endpoints of any diameter.
CS-23
Add to your notes
The endpoints of any diameter divide a circle into two congruent arcs.
Semicircle:
Arc formed by the endpoints of any diameter.
measure of a semicircle = 180
Arc length of a semicircle = ½  C b)
Find mABC.
90 A B C a)
Find mA.
180
(Inscribed  Thm.) A
(Inscribed  Thm.)
mABC = 290
mA = ½180
mABC = 180
mA = 90

9. In the figure at right, U has a diameter GR.
CS-24 G
In the figure at right, U has a diameter GR. I
a) Find mF and mRIG. U
mGR = 180°
(semicircle = 180°) F
(Inscribed  Thm.)
(Inscribed  Thm.) R
mF = ½180
mRIG = ½180
mF = 90
mRIG = 90
b) What conclusion can you draw about an angle inscribed in a semicircle? Write your conjecture in one or two complete sentences.
The angle inscribed in a semicircle is always a right angle (its measure is always 90).

10. Continue working
on CS , 29
and MCFR #23-27

11. CS 21 works better on the document camera!!!!!! (Next 6 slides!)
1) Outline each of the inscribed angles (C,D, & E) and its intercepted arc with a different color. Name the arc that each angle intercepts. .
C intercepts _______ D intercepts _______
E intercepts _______ AB
CS 21 works better on the document camera!!!!!! (Next 6 slides!) AB AB
2) Trace C on your tracing paper. Place it over D and compare their sizes. Do the same for E. What appears to be true about the angle measures?
3) Make another copy of C on your tracing paper so that it is adjacent to the first copy; that is, they share a vertex and share a side. What appears to be true about the sum of the two copies? (You can use the angles at the bottom to verify your thoughts!)

12. All three angles have the same measure.
CS-21
1) Outline each of the inscribed angles (C,D, & E) and its intercepted arc with a different color. Name the arc that each angle intercepts. .
C intercepts _______ D intercepts _______
E intercepts _______ AB
2) Trace C on your tracing paper. Place it over D and compare their sizes. Do the same for E. What appears to be true about the angle measures?
All three angles have the same measure.
3) Make another copy of C on your tracing paper so that it is adjacent to the first copy; that is, they share a vertex and share a side. What appears to be true about the sum of the two copies? (You can use the angles at the bottom to verify your thoughts!)

13. All three angles have the same measure.
CS-21
2) Trace C on your tracing paper. Place it over D and compare their sizes. Do the same for E. What appears to be true about the angle measures?
All three angles have the same measure.
3) Make another copy of C on your tracing paper so that it is adjacent to the first copy; that is, they share a vertex and share a side. What appears to be true about the sum of the two copies? (You can use the angles at the bottom to verify your thoughts!)
2 (mC) = _________  mC = _________
90
45

14. For all 3 angles, the intercepted arc is AB
CS-21
4. Compare the measure of the intercepted arc to each of the inscribed angles and write a conjecture that states the relationship.
For all 3 angles, the intercepted arc is AB
The measure of the inscribed angle is ½ the measure of the intercepted arc.

15. H intercepts _______ J intercepts _______ K intercepts _______F G
120°
CS-21
5. Outline each of the inscribed angles (H, J, & K) and its intercepted arc with a different color. Name the arc that each angle intercepts.
H intercepts _______ J intercepts _______
K intercepts _______ FG FG FG
6. Based on your findings from Circle 1 above, what should the angles measure?
mH = _______; mJ = _______; mK = _______
60
60
60

16. The sum of the three angles is 180.J K F G
120°
CS-21
7. Trace H and verify that it is equal to both J and K. Now, trace J and K on your tracing paper so that they are adjacent to H. What appears to be true about the sum of the three angles?
The sum of the three angles is 180.
mH + mJ + mK = _______
3(mH) = _______ (substitution)
mH = _______
180
180
60
8. Does this verify your conjecture?
Yes. We said the measures of these inscribed angles were each 60.