Hampton High School
Geometry Lesson Plan – Circles – Central Angles and Inscribed Angles
Michelle Bousquet
Context: This lesson is designed for a 90 minute Geometry class at Hampton High School. The
class contains a maximum of 19 students. This is the first of three lessons on angle measures of
circles. In this lesson, the students will learn basic vocabulary of circles and make calculations
based on central angles and vertices on circles.
SOL: G.11 The student will use angles, arcs, chords, tangents, and secants to:
a) investigate, verify, and apply properties of circles;
b) solve real-word problems involving properties of circles; and
c) find arc lengths and areas of sectors in circles
Student Grouping: Whole, Small groups, individual work
Objective: By the end of the class period, the students will be able to accurately complete
worksheets on central angle and inscribed angle measures of circles, as checked by the teacher.
Materials Needed:
Warm Up
Circle Vocabulary Worksheet
Colored Hefty Plates – 1 for each student
White Hefty Plates – 1 for each student
Ruler or straightedge – 1 for each student
Scissors – 1 pair for each student
Angle Ruler – 1 for each student
Piece of yarn about 1.5 feet long – 1 for each student
Push pins – 3 for each student
Circles: Central Angles and Inscribed Angles Worksheet
10-2 Practice Angles and Arcs – Glencoe/McGraw-Hill
10-4 Skills Practice Inscribed Angles – Glencoe/McGraw-Hill
Content Instructional Strategies:
1. Warm up: The students will complete a warm up containing questions from previous
Virginia Standards of Learning tests. While the students are completing the warm-up,
take attendance. After going over the warm up, briefly introduce circles.
15 minutes
2. Pass out the Circle Vocabulary Worksheet. Ask the students to define the terms
themselves first before going over the definition.
10 minutes
3. Pass out one colored plate, one white plate, a ruler, a pair of scissors, a piece of yarn,
three push pins, and an angle ruler to each student. Have the students create two
diameters of each circle to find the center. The students will cut ONE radius in each plate
and fit the plates together so that the 36 notches interlock with each other. Pass out the
Circles: Central Angles and Inscribed Angles worksheet and go through the steps with
the students to help them answer the questions. They will discover for themselves how to
find the central angle and inscribed angle measure when given an arc measure.
45 minutes
4. Pass out the 10-2 Practice Angles and Arcs and the 10-4 Skills Practice Inscribed Angles
worksheets. The students will work individually or in groups of two or three to complete
the two worksheets. For the Practice Angles worksheet, the students should only solve
problems 1-12. The questions unanswered after 15 minutes will be assigned for
homework.
15 minutes
5. Exit Slip:
Answer:
Evaluation: By accurately completing the practice worksheets as checked by the teacher, the
teacher will have a good idea as to what concepts the students are still struggling with.
Differentiation and Adaptations: If there is not as much time as anticipated, the class can finish
the worksheets for homework or the teacher can do the questions with the class. Faster students
will work in their groups to help the rest of the class. If there is a shortened class period, the
circle manipulatives can be pre-made to save time.
If some of the students discover the patterns and rules faster than other students, those students
can work to complete the worksheets without testing the rules with plates.
Name: __________________________________________________
Circle Vocabulary
Radius:
Diameter:
Chord:
Circumference:
Arc Length:
Central Angle:
Minor Arc:
Major Arc:
Semicircle:
Date: _____________
Name:__________________________________________
Date:___________________
Circles: Central Angles and Inscribed Angles
1. Circles are __________ degrees around.
2. The two interlocking plates have 36 notches around. This means that each notch
represents _________ degrees.
3. What is the arc measure when there are 9 white notches showing?
___________
4. A central angle is an angle formed at the center of a circle. Using the angle ruler, what
is the central angle measure when there are 9 white notches showing?
____________
5. What is the arc measure when there are 12 white notches showing?
__________
6. Using the angle ruler, what is the central angle measure when there are 12 white notches
showing?
____________
7. What is the relationship between an arc measure and a central angle measure?
8. An inscribed angle is an angle with its vertex on the circumference of a circle. Using an
angle ruler, what is the measure of an inscribed angle when there are 9 white notches
showing?
______________
9. Using an angle ruler, what is the measure of an inscribed angle when there are 12 white
notches showing?
_____________
10. What is the relationship between inscribed angles, central angles, and arc measures?
Answer Key:
Circles: Central Angles and Inscribed Angles
1. 360
2. 10
3. 90 degrees
4. 90 degrees
5. 120 degrees
6. 120 degrees
7. they are equal
8. 45 degrees
9. 60 degrees
10. The measure of an inscribed angle is ½ the measure of its corresponding central angle or
arc measure
NAME ______________________________________________ DATE
____________ PERIOD _____
10-2 Practice
Angles and Arcs
ALGEBRA In !Q, A
!C
! and B
!D
! are diameters. Find each
E
measure.
1. m!AQE
2. m!DQE
A
3. m!CQD
4. m!BQC
5. m!CQE
6. m!AQD
D
(5x " 3)#
(6x " 5)#
(8x " 1)#
B
In !P, m"GPH ! 38. Find each measure.
!
!
7. mEF
8. mDE
!
10. mDHG
!
11. mDFG
!
12. mDGE
!
14. QR if m!QZR ! 60
T
S
P
Z
Q
!
15. PQR if m!PZR ! 150
G
P
F
The radius of !Z is 13.5 units long. Find the length of each arc
for the given angle measure.
!
13. QPT if m!QZT ! 120
H
D
E
!
9. mFG
C
Q
R
!
16. QPS if m!QZS ! 160
HOMEWORK For Exercises 17 and 18, refer to the table,
which shows the number of hours students at Leland
High School say they spend on homework each night.
17. If you were to construct a circle graph of the data, how many
degrees would be allotted to each category?
Homework
Less than 1 hour
8%
1–2 hours
29%
2–3 hours
58%
3–4 hours
3%
Over 4 hours
2%
18. Describe the arcs associated with each category.
©
Glencoe/McGraw-Hill
550
Glencoe Geometry
NAME ______________________________________________ DATE
____________ PERIOD _____
10-4 Skills Practice
Inscribed Angles
!
!
!
In !S, mKL ! 80, mLM ! 100, and mMN ! 60. Find the measure
of each angle.
K
1
6
2. m!2
1. m!1
2
S
M
N
4. m!4
5. m!5
6. m!6
3
4
5
3. m!3
L
ALGEBRA Find the measure of each numbered angle.
7. m!1 ! 5x " 2, m!2 ! 2x # 8
8. m!1 ! 5x, m!3 ! 3x # 10,
m!4 ! y # 7, m!6 ! 3y # 11
B
F
A
1
2
J
3
4
2
G
U
C
1
I
6
5
!
Quadrilateral RSTU is inscribed in !P such that mSTU ! 220
and m"S ! 95. Find each measure.
9. m!R
U
T
10. m!T
P
R
11. m!U
!
12. mSRU
!
13. mRUT
!
14. mRST
©
Glencoe/McGraw-Hill
561
S
Glencoe Geometry
Lesson 10-4
H