Division
School
Teacher
Time & Dates
I. OBJECTIVES
A. Content
Standards
B. Performance
Standards
C. Learning
Competencies/
Objectives
(Write the code
for each LC)
II. CONTENT
A. Subject
Matter
III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide Pages
2. Learner’s
Material Pages
3. Textbook
Pages
4. Additional
Materials from
LR Portal
B. Other Learning
Resources
IV. PROCEDURES
A. Reviewing
previous
lesson or
presenting the
new lesson
ISABELA
LAPOGAN INTEGRATED SCHOOL
LUISA FRANCISCO-GARCILLAN
Week 7 Day 4
Grade Level
Learning Area
Quarter
7
MATHEMATICS
THIRD
The learner demonstrates understanding of key concepts of geometry of
shapes and sizes, and geometric relationships.
The learner is able to create models of plane figures and formulate and
solve accurately authentic problems involving sides and angles of a
polygon.
Illustrate a circle and the terms related to it: radius, diameter chord, center,
arc, chord, central angle, and inscribed angle (M7GE-IIIg-1)
 Determine the relationship between a central angle and its
intercepted arc
 Discover the relationship between an inscribed angle and its
intercepted arc
 Appreciate the relationship of central angle, inscribed angle and its
intercepted arc in our daily life.
GEOMETRY
Relationship Between Central Angle, Inscribed Angles and Its Arc
Values : Truthfulness and friendship
Teaching Guide pp. 286 – 289
Learning Module pp. 233 – 236
ID NO. 1906 :EASE Module 1 Circles
https://lrmds.deped.gov.ph/detail/1906
Textbook : Exploring Mathematics III, Geometry, pp. 453-459 , Orlando A.
Oronce and Marilyn O. Mendoza
Learner’s Expected
Teacher’s Activity/ies
Response/s
Recall the previous lesson.
Show a jumble words:
1.CAR
2. BEDRIINSC
3. CLEIRC
4. ANGEL
5. TREENC
ANSWER:
1. ARC
2. INSCRIBED
3. CIRCLE
4. ANGLE
5. CENTER
These are the parts of a circle.
This time, let us do a group activity.
B. Establishing a
purpose for
the lesson
Activity:
In a piece of manila paper, draw a circle having
Group 1: 2 diameters
Group 2: 4 diameters
Group 3: 8 diameters
What angle do you recognize?
A central angle
C. Presenting
examples/
instances of
the new
lesson
How was the circle divided in a) 2 diameters b)
4 diameters c) 8 diameters?
The circle was divided
equally.
a) The circle was
divided into four
b) It divided into 8
parts.
c) It divided into 16
parts
What comes up to your mind when hear the
word central angle?
An angle whose
common vertex is the
center of the circle.
How can we relate the central angle to its
intercepted arc?
The radii of circle will be
the sides of angle so all
the angles form in the a
circle are equal.
Show an illustration on the board.
Fig 1
fig 2
fig 3
Based on the figure, how will you establish the
relationship of central angle and its arc?
Discuss pages 453 454 and of the Exploring
Mathematics III and pages of Eas 14 – 16 Ease
Module 1 Circles and Learning Module
D. Discussing
new concepts
and practicing
new skills #1
 From the figure above, we see that AC and BD
are perpendicular to each other and intersect
at the center of O.
 In figure 1, shows the four equal divisions of
the arcs and the central angles. Since AC and
BD are perpendicular, each central angle in
this figure is a right angle and its measure 90
degrees.
 We also know that regardless of the size of the
circle its measure is 360 degrees, then each
arc has a measure of 90 degrees.
 In figure 2, the segments AC, BD, HF, and GE
divide the circle into eight equal parts and
eight equal angles. Hence, each arc has a
measure 45 degrees.
 In figure 3, the segments AC, BD, IM, JN, PK,
and QL divide the circle into twelve equal parts
and twelve central angles, hence each arc has
a measure of 30 degrees.
 This inquiry leads to the Central AngleIntercepted Arc Postulate
 The measure of a central angle of a circle is
equal to the measure of its intercepted arc.
Another study of the angles in a circle and in
determining their measures, it is important to
determine the intercepted arc(s) of the given
angle. To understand better, let us see some
examples.
From the figure, we can
see that AC and BD are
perpendicular to each
other and intersect at the
center O.
In the figure, the arc in the interior of the angle
is the intercepted arc of the angle.
The intercepted arc of BAC is
the minor arc AC.
In the given figures above of inscribed angles
the following holds:
 DEF is an inscribed angle
 DEF intercepts arc DF
b) In figure 2,  PST is an inscribed angle,
 PST intercepts arc PT
c) In figure 3,  BAC is an inscribed angle
 BAC intercepts arc BC
a) In figure 1,
 Every angle whether in a circle on in any plane
is associated with a unique number defined as
its measure. If the measure of a central angle
is equal to the measure of its intercepted arc,
the next theorem will tell us how to find the
measure of the inscribed angle.

Theorem: Inscribed angle Theorem
The measure of an inscribed angle is
equal to one half the measure of its intercepted
arc.
It means that in the given figure,
mDEF  12 mDF
D
F
O●
E
For further illustrations, present a video clip that
will show and explain the relationship of central
and inscribed angles with respect to its
intercepted arc, which can be downloaded on
the link below.
https://youtube/rOvjqPCU_K4
https://www.youtube.com/watch?v=xMUOcAnb
K1c
E. Discussing
new concepts
and practicing
new skills #2
After the video clipping, ask the following:
1. How will you relate the intercepted arc to its
angle?
The
measure
of
intercepted arc will based
the angles form in the
circle.
2. What is the difference between the
inscribed angle theorem and the central
angle postulate?
The measure of a central
angle of a circle is equal
to the measure of its
intercepted arc while the
measure of an inscribed
angle is equal to one half
the measure of its
intercepted arc.
Based from the figure, complete the table
below:
F. Developing
mastery
Fig 1
Figure
G. Finding practical
applications of
concepts and
skills in daily
living
No. of
Congruent
Central
Angles
fig 2
No. of
Congruent
Arcs
Fig
ure
No.
of
Cong
ruent
Centr
al
Angle
s
No.
of
Cong
ruent
Arcs
Measur
e of
Each
Central
angle
Meas
ure
of
each
Arc
1
4
4
90
90
2
8
8
45
45
3
12
12
30
30
fig 3
Measure
of Each
Central
angle
Measure
of each
Arc
1
2
3
Ask a student to have an example that relate
central angle theorem and inscribed angle
theorem in our daily life.
Answers may vary.
Ask a learner to make a conclusion about the
topic.
H. Making
generalization
and abstractions
about the lesson
Who can make a conjecture about the
relationship of central angle and its intercepted
arc?
How about an inscribed angle and its
intercepted arc?
The measure of
a
central angle of a circles
equal to the measure of
its intercepted arc.
The measure of an
inscribed angle is onehalf the measure of its
intercepted arc.
Conduct a short Quiz.
Answer the following questions.
1. In the figure below, measure of angle
IPE is 45 degrees, find
a. Measure of arc IE
b. Measure of arc LE
c. Measure of arc LI
d. Measure of angle LPI
I. Evaluating
learning
I
L
P
E
2. Given the figure below, measure of arc AC is
100, measure of arc AR is 80 and measure of
angle ECR is 35. Find
a. measure of angle CEA
b. measure of arc ER
c. measure of angle R
d. measure of angle E
Differentiated Instruction will be introduce here:
J. Additional
activities for
application or
remediation
V. REMARKS
VI. REFLECTION
A. No. of learners
who earned
80% on the
formative
assessment
B. No. of learners
who require
additional
activities for
remediation
C. Did the remedial
lessons work?
No. of learners
who have
caught up with
the lesson.
D. No. of learners
who continue to
require
remediation
 For advance students, let them design
their own “dream” yard, park or golf
course that relate the inscribed and
central angles
 For all the students, let them do their
journal writings and reflections using
teacher notes from the discussion.
E. Which of my
teaching
strategies
worked well?
Why did these
work?
F. What difficulties
did I encounter
which my
principal or
supervisor can
help me solve?
G. What innovation
or localized
materials did I
use / discover
which I wish to
share with other
teachers?
Prepared by:
LUISA FRANCISCO-GARCILLAN
Mathematics Teacher
Checked and Observed by:
ROSALINDA B. GARCILIAN- RODEO
School Principal
GROUP ACTIVITY SHEET
Group 1.
A
D
O
B
C
Group 2:
A
H
E
D
O
G
B
F
C
Group 3:
A I
Q
P
D
N
I
J
B
K
O
M
C
L