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QUARTER II
Week 4
Grade Level: 10
Date:
Day: 1
__________________
Demonstrates understanding of key concepts of circles and
Content Standard
coordinate geometry.
1. Is able to formulate and find solutions to challenging
situations involving circles and other related terms in
different disciplines through appropriate and accurate
Performance representations.
Standard
2. Is able to formulate and solve problems involving
geometric figures on the rectangular coordinate plane
with perseverance and accuracy.
Competency 23: Proves theorems related to chords, arcs,
Competency
central angles, and inscribed angles. (M10GE-IIc-d-1)
I. OBJECTIVES
Knowledge: Identifies the theorems related to arcs and chords
Skill: Proves theorems related to arcs and chords
Attitude: Demonstrates cooperation during group activities in
proving theorems related to arcs and chords.
II. CONTENT Theorems on Chords and Arcs
III. LEARNING RESOURCES
A. References
a) Teacher’s Teacher’s Guide (TG) in Mathematics 10, pp. 130 – 139
Guide Pages
b) Learner’s Learner’s Module (LM) in Math 10, pp. 140 - 149
Materials
Pages
c) Textbook E – Math Worktext in Mathematics pp. 162 - 171
Pages
d) Additional Attachment
Materials
e) Learning EASE Module 1 on Circles, pp. 2 – 21
Resources
(LR) portal
B. Other http://www.mathopenref.com/arc.html
Learning http:// www.mathopenref.com/chord.html
Resources www.mathopenref.com/circlecentral .html
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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IV. PROCEDURES
A. Reviewing or Note to the Teacher:
presenting the Have a review on the theorem “In a circle or in
new lesson congruent circles, two minor arcs are congruent if and
only if their corresponding central angles are congruent.
Review also on SSS, ASA, and SAS Postulates.
Review CPCTC
B. Establishing a In this Lesson , you will learn the theorems related to arcs and
purpose for the chords
lesson
C. Presenting Draw two congruent circles on the board.
examples of the Ask a student to draw a chord in each circle. Assume that
new lesson the measure of the chords are equal.
Ask another student to measure a 60° angle on each
circle.
Label the points with letters.
C E
D F
A H
Ask the following questions:
a. What did you observe with the two circles?
Expected Answer: Answer may vary.
b. Can you identify the chords? What are these?
Expected Answer: Yes. CD, EF
c. Can you identify the minor arcs? What are these?
Expected Answer: Yes. CD ≅ EF
D. Discussing new
concepts and
practicing new
skills #1
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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(Refer to LM page 144-146 for the discussion)
E. Discussing new
concepts and
practicing new
skills #2
STATEMENTS REASONS
1. Given
2. All radii of a circle
are equal.
3. SSS (Side-Side-Side
Theorem)
4. Corresponding Parts
of Congruent Triangles
are Congruent (CPCTC)
5. Congruent central
angles intercept
congruent arcs.
F. Developing
Mastery
Refer to Attachment for the answer.
G. Finding How can you apply your learnings in your daily life? Can
practical you give an example?
applications of
concepts and
skills in daily
living
H. Making Guide Questions for Generalization:
Generalization (To be answered by the students)
s and What was the theorem being discussed?
abstractions (Expected answer:
about the
lesson
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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I. Evaluating
learning
J. Additional
Activities for
application or
remediation
V. REMARKS
VI. REFLECTION
A. No. of learners A. ____ No. of learners who earned 80% in the evaluation
who earned 80% in
the evaluation
B. No. of learners B. _____ No. of learners who require additional activities for
who require remediation
additional
activities for
remediation
C. Did the C. Did the remedial lessons work? ______ No. of learners
remedial lessons who have caught up the lesson
work? No. of
learners who have
caught up the
lesson
D. No. of learners D. _____ No. of learners who continue to require remediation
who continue to
require
remediation
E. Which of my Strategies used that work well:
teaching strategies ____ Group Collaboration
worked well? Why ____ Games
did these work? ____ Powerpoint Presentation
____ Answering preliminary activities/exercises
____ Discussion
____ Case Method
____ Think-Pair-Share
____ Rereading of Paragraphs?Poems/Stories
____ Differentiated Instruction
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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____ Role Playing/Drama
____ Discovery Method
____ Lecture Method
Why?
____ Complete IMs
____ Availability of Materials
____ Pupil’s eagerness to learn
____ Group member’s Cooperation in doing their tasks
F. What difficulties ____ Bullying among pupils
did I encounter ____ Pupil’s behavior/attitude
which my principal ____ Colorful IM’s
and supervisor ____ Unavailable Technology
help me solve? ____ Equipment (AVR/LCD)
____Science/Computer/Internet Lab
____ Additional Clerical works
____ Reading Readiness
G. What
innovation or
localized I
used/discover
which I wish to
share with other
teacher?
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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ATTACHMENT
Developing Mastery:
STATEMENTS REASONS
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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ANSWER KEY:
Developing Mastery:
STATEMENTS REASONS
1. AB ≅ CD 1. Given
2. ∠DPC ≅ ∠APB 2. Congruent cetral angles intercept
congruent arcs.
3 PD ≅ PC ≅ PA≅ PB 3. All radii of a circle are congruent.
4. DPC ≅ APB 4. SAS (Side – Angle – Side Theorem)
4. Correspondinf Parts of Congruent
5. AB ≅ CD Triangles are Congruent (CPCTC)
Evaluation:
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
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REFERENCES
A. DepEd INSTRUCTIONAL MATERIALS:
EASE Modules Year 3, Module 1: Circles , pp. 1-21
Callanta, M., & et. al. (2015). Mathematics-Grade 10 Learner’s Module (1st Ed.).
Pasig City: DepEd-IMCS
B. BOOKS AND OTHER REFERENCES
K to 12 Curriculum Guide Mathematics. (2012). Department of Education,
Philippines;
Oronce, O. & Mendoza, M. E-Math, Worktext in Mathematics, pp. 162 - 171
C. INTERNET SOURCES:
www.google.ph.com
http://www.mathopenref.com/arc.html
http:// www.mathopenref.com/chord.html
www.mathopenref.com/circlecentral .html
Prepared by: Maria Fatima M. Emperado , Ayungon Science High School, Ayungon District 2
