Republic of the Philippines
Department of Education
Region II
Solana South District
Solana National High School
Nangalisan, Solana, Cagayan
LESSON PLAN IN MATHEMATICS 10
QUARTER 2 – MODULE 19
I. LEARNING OBJECTIVES
At the end of the lesson, the students should be able to:
a) Define arcs, central angles and chords,
b) Systematically deduces the relationships between arcs, and central angles,
c) Apply the arc addition postulate involving in solving problems involving circles.
II. SUBJECT MATTER
A. Topic:
B. References:
The Relation among Arcs and Central Angles
MATHEMATICS – GRADE 10
Quarter 2 – Module 19: The Relation among Chords, Arcs, Central
Angles, and Inscribe Angles
First Edition, 2020
M10AL Ila-1
C. Materials:
PowerPoint, BLACKBOARD
D. Value Integrated:
Critical Thinking, Attentiveness, Cooperation and Participation
E. Value Statement:
“Draw a circle around yourself – invite people in or keep them out. We
are the creators of our social geometry.” – Rachel Wolchin
III. PROCEDURE
TEACHER’S ACTIVITY
I. PRELIMINARIES
Greetings
Prayer
Goodmorning Class!
May I request to everyone to please
stand for our today’s session prayer.
STUDENT’S ACTIVITY
Goodmorning Sir!
(the students will stand for the prayer)
You may sit class!
Thank you Sir!
Checking of
attendance
Anyone who is not around?
None sir!
May I ask the class secretary to please
check the attendance of your classmates
and give me the summary of it later?
Noted sir!
Presentation of
house rules
Thank you!
Class be settled down. As we will have
our Math session today, I will present to
you the house rules.
(video presentation about classroom
rules)
Does these rules clear to you?
Yes Sir!
Activity
Anyway, class, we will start our session
today with a game activity. This game
called “IN A LEMON MATHREE”.
How to play this game?
o Your row will be your group, so
it means that there are three
groups.
o Set of jumbled letters will be
presented through slides once in
a while and each group will try
to decipher or understand the
words which are related to circle
while playing the song “Lemon
Tree”.
o There are pictures that will be
presented with the jumbled
letters which serves as you clue.
o Raise your slate within ten
second if you already wrote the
answer.
o Every correct answer is
equivalent to two (2) points.
Did you get it class?
Yes sir!
Let us start the game.
The sequence of the jumbled words are
as follows:
1)
2)
3)
4)
5)
RDHCO
LESAGN
TLRAENC
CRSA
EIRCLMSIEC
(after the game the teacher will
acknowledge their scores)
Analysis
1)
2)
3)
4)
5)
CHORD
ANGLES
CENTRAL
ARCS
SEMICIRCLE
How did you find the game? It is fun?
Did you enjoy it?
Yes, we did sir!
So based on the game we had, are you
familiar with those words or
terminologies?
Yes sir!
Can you visualize or picture out them?
Yes sir!
Those words you have encountered in
the game has something to do with
Circle. Those terms are connected with
Circle.
Using those words, what do you think is
our lesson today?
Abstraction
Very Good! Our lesson for today is The
Relation Among Chords, Arcs and
Central Angles.
Goodmorning once again class!
Before we are going to dig with our
topic today, I would like to present to
you the learning objectives for today.
But just for the meantime, kindly fix
you chairs and tables and pick up the
rappers around you.
Anyway going back to our learning
objectives.
At the end of the discussion, you as a
learning should be able to:
(1) Define arcs, central angles and
chords,
(2) Systematically deduces the
relationships between arcs, and
central angles,
(3) Apply the arc addition postulate
involving in solving problems
involving circles.
We will start our discussion by
reviewing some of the terms related to
circle. But before that we are going to
Sir, it is all about arcs, chords and
central angles.
define first the term circle in geometry?
A circle is a set of all points with the
same distance from a fixed point
called the center. The center is used to
name a circle.
Very good! As you can see the figure
that is flashed on the screen, there is a
circle with numerous lines. And those
lines has a specific name.
(figure 1. The first figure to be flashed)
Figure 2. the finished figure after discussing
about the related terms in circle.
So let as start with the radius. Now,
what do you know about it?
Great! Next to define is Diameter. What
is a Diameter?
A radius of a circle is a segment
whose endpoints are the center and a
point on the circle. It is the distance
from the center to any point on the
circle.
Awesome! Now, what is a Chord?
A diameter of a circle is a chord that
passes through the center of the circle.
Very good! How about Tangent?
It is the longest chord of a circle and
its length is twice as long as its radius.
A chord of a circle is a line segment
that has its endpoints on the circle.
Awesome! Last term is secant. Who can
give the definition of secant?
Yes Mr/Ms…….
A tangent is a line, a segment, or a ray
that intersects a circle at exactly one
point, and the point of intersection is
called the point of tangency.
Very good! So class these terms have
something to do with circles but we are A secant is a line, a segment, or a ray
not going focus on these terms, however that intersects a circle at exactly two
some of these terms will be tackled
points.
about again.
Now, let us proceed to our main topic
and it is all about Arcs, Chords and
Central Angles.
(The teacher will use the figure for his
discussion about Arcs, Chords and
Central Angles.)
Figure 1.
Let us begin with Arcs. Kindly read
what is arc?
Thank you! (the teacher will explain
about it)
There are three classifications of arc,
the first one is Semicircle. What is
semicircle?
Great! The second one is Minor Arc.
What is it all about?
Very Good! If there is Minor Arc, there
An arc is a part of a circle between
any two points. It is measured in
terms of degrees. A circle is in itself
an arc that measures 360°.
A semicircle is an arc which is 𝑜𝑛𝑒ℎ𝑎𝑙𝑓 of a circle. It measures exactly
180°.
is also a Major Arc. What is Major Arc?
Great! A minor arc is named using the
two endpoints of the arc. A semicircle is
named using three points. The first and
the third points are the endpoints of the
diameter and the middle point is any
point of the arc between the endpoints.
In cases where there are only two points
given on a circle, the semicircle is
named using the two points. Lastly, a
major arc is named using three points.
The first and the third are the endpoints
and the middle point is any point on the
arc between the endpoints.
A minor arc is less than a semicircle
and its measure is between 0°.
A major arc is greater than a
semicircle which measures between
180° and 360°.
Did you get it class?
Now, let us proceed to Central Angle.
What do you know about?
Very good! (the teacher will use the
figure to show where is a central angle)
After knowing the central angle, we are
going to define next the Intercepted
Arc. Mr/Ms……
Yes Sir!
A central angle of a circle is an angle
formed by two radii and its vertex is
the center of the circle.
Good job! (the teacher will explain well
the Intercepted Arc)
For you to have deep knowledge with
regards to our topic which is the relation
among Arcs and Central Angle, we are
going discuss about the “Sum Of
Central Angles”
An intercepted arc is created when
lines or subsets of a line cuts across a
section of the circumference of a
circle. The intersection of the lines or
subsets of it are on the circle, thus
forming an inscribed angle.
Mr/Ms…. Read the about Sum of
Central Angles……..
Thank you! (the teacher will explain it
well to his students so that they can
follow and do it well with their own)
Sum of Central Angles: The sum of
the measures of the central angles of a
circle with no common interior points
is 360°. In the figure, ∠1, ∠2, ∠3, and
∠4 are examples of central angles
without common interior points.
We have here an example that shows
the relationship between the central
angle intercepting the arc of a circle.
Did you get it class?
Now, we are going to explore the Arc
Addition Postulate.
Ms/Mr………can you what is flashed
on the screen?
Yes sir!
Thank you! (the teacher will explain it
well)
Arc Addition Postulate: The measure
of an arc formed by two adjacent nonoverlapping arcs (arcs that share
exactly one point) is equal to the sum
of the measures of these two arcs.
Any questions or clarifications class?
Have you discovered the relationship?
None Sir!
among arcs and central angles So what
is the relationship between the two?
Yes sir!
Very good! So before we proceed to
your task/or another activity. We will
just have a summary on what you have
learned today. So please listen carefully
Generalization
The central angle of an arc is the
central angle subtended by the arc.
Application
Triads Activity: (Great Test 3 in one)
What to do?
Form group that contains 3 members. Work the task together. You are given 5
minutes to finish this task. You can answer this task by applying the Arc
Addition Postulate.
IV. EVALUATION
A. Directions: Apply the arc addition postulate. Solve for what is ask. Put this in ½ crosswise.
B. Directions: Identify what is being asked in the given items. Refer to ⊙𝐶
V. ASSIGNMENT
Form a group of 3 members, and simply work together with the given tasks. In one paragraph, do the
following format:
In the first sentence, define arcs in your own words. In second sentence, define central angles. In the
third sentence, present an examples of the two in real life. Then in the fourth paragraph, answer the
question “How are arcs and central angles related to each other”. In fifth paragraph, cite an example.
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Prepared by:
MARK ROLANDO S. TABBU
Bachelor of Secondary Education
Major in Mathematics
Field Study Sudent