I. OBJECTIVES
A. Content Standards
The learner demonstrates understanding of key concepts of geometry of shapes
and sizes, and geometric relationships.
B. Performance
Standards
The learner is able to create models of plane figures and formulate and solve
accurately authentic problems involving sides and angles of a polygon.
C. Learning
Competencies
Derives inductively the relationship of exterior and interior angles of a convex
polygon. (Quarter 3, MELC #39)
At the end of the lesson, the students will be able to:
(1) derive inductively the relationship of interior and exterior angles of a
convex polygon;
(2) determine the sum of the interior angles of a convex polygon;
Objectives
(3) determine the sum of the exterior angles of a convex polygon;
(4) determine the measure of the interior angle of a regular polygon; and
(5) Determine the measure of the exterior angle of a regular polygon.
II. CONTENT
III. LEARNING
RESOURCE
References
IV. PROCEDURE
Preparation
The Sum of the Interior and Exterior Angles of a Polygon
`
https://www.geeksforgeeks.org/polygon-formula/
https://www.sparknotes.com/math/geometry1/polygons/section2/
Resources
Daily Routine
A. Prayer
B. Greeting
C. Checking of Cleanliness
D. Checking of Attendance
E. Reminder (Health Protocol)
INTRODUCTION
The teacher will ask the following and will randomly
call students to share their answers in the class.
I. Identify whether the following figures is a
POLYGON or NOT a POLYGON.
POLYGON
NOT A POLYGON
II. WHY are the following figures polygons?
Answers:
- closed figures
- straight sides
- has at least three sides
- planes
NOTE:
A plane is a flat surface that extends forever in
two dimensions, but has no thickness.
III. WHY are the following figures not polygons?
Answers:
- have curve lines
- NOT all sides are
straight lines
NAMING POLYGONS ACCORDING TO THE
NUMBER OF SIDES
Cut Outs
PPT
DEVELOPMENT
The teacher will introduce the lesson using PPT
constructivism approach. She will guide the students on
how to determine the sum of the interior angles of a
polygon inductively. To do this, she will first ask the
students to follow the given instructions on each
example, and let them realize a pattern that could help
them in solving for the sum of the interior angles of a
polygon.
Example 3:
Afterwards, the teacher will ask the students to
determine the number of triangles formed on each
polygon, and use this information in finding the sum of
the interior angles of the given polygon. The teacher
will then write on the board the following answers
gathered from the students.
Polygon
No. of
Sides
Number
of
Triangles
Formed
Sum of the interior
angles
Triangle
3
1
1 x 1800 = 1800
Quadrilateral
4
2
2 x 1800 = 3600
Pentagon
5
3
3 x 1800 = 5400
Hexagon
6
4
4 x 1800 = 7200
Heptagon
7
5
5 x 1800 = 9000
Octagon
8
6
6 x 1800 = 1,0800
Nonagon
9
7
7 x 1800 = 1,2600
The teacher will then ask the following questions.
(1) Have you observed any pattern in finding the sum of
the interior angles of any given convex polygon?”
(2) If so, what is it then?
Possible answers of the students:
(1) Yes
(2) If we let the number of sides of any convex polygon
be N, then we can represent the sum of the interior
angles of any convex polygon as:
(N - 2) x 1800
Teacher : Very Good! That is a very keen observation!
The teacher will now then help the students to determine
the sum of the exterior angles of any convex polygon
inductively, and will call students randomly to share
with the class their observations.
After these observations, the teacher will then guide the
students in discovering how to determine the measure of
the interior and the exterior angles of a regular polygon.
ENGAGEMENT
Name the following polygons and find the sum of its
interior angles.
(1)
(4)
ASSIMILATION
(2)
(3)
(5)
Find the measure of the interior and exterior angles of
the following polygons.
(1)
(2)
(3)
(4)
(5)
Wrap up
Feedback / Assessment
Closure/Reflection /
Assignment
V. REMARKS
VI. REFLECTION
A. No. of learners who
earned at least 80% on the
formative assessment
B. No. of learners who
require additional
PPT
Find the sum of the interior angles, and measure of each
interior and exterior angle of a decagon.
PPT
Homework:
PPT
Given the following n-side polygons, find the following:
(i) measure of each interior angle;
(ii) measure of each exterior angle;
(iii) sum of the interior angles of each polygon.
(1) hendecagon
(2) dodecagon
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
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
teacher?