POLYGONS.pptx

1
Objectives:
In this lesson; you are expected to:
1. Illustrate polygons
a.) convexity
Polygons and Other Related
Terms

i2
Activity 15
Definition of a Polygon
The following are polygons:
The following are not polygons:
Which of these are polygons?
Activity 15
Definition of a Polygon
The following are polygons:
The following are not polygons:

i3
What is then a polygon?
a.
e.
b.
c.
d.
f.
g. h.

i4
“Polygon” comes from the Greek words
“poly”, which means “many”
“gon” which means “angles.”
Polygon is a closed plane figure formed by three
or more segments such that each segment
intersects exactly two others only at the vertices,
one at each endpoint, and no two segments with
a common endpoint are colinear

i5
` Polygons are named by
writing their consecutive
vertices in order
ABCDE
Or AEDCB
Or CDEAB
Or CBAED , etc.
for the figure on the right.

i6
Consecutive sides - two
sides of a polygon that
share a common endpoint.
Consecutive angles - two
angles whose vertices are
endpoint of the
consecutive sides.

i7
Included side – the
common side of two
consecutive angles
Included angle the angle
whose vertex is the
common endpoint of two
consecutive sides

i8
Diagonal is a
segment joining
non-consecutive
vertices.

i10
List down the sides,
vertices and number of
distinct diagonals of
each of the following
polygons
Polygon 1

i11
List down the sides,
vertices and number of
distinct diagonals of
each of the following
polygons
A
R T
Polygon 2

i12
Answer Checkpoint 1 letter a and b on
page 6 of Module 5

i13
Are these polygons?
Set A
Set B
Yes
Yes

i14
What is the difference between the two sets of
polygons?
Set A
Set B
Convex Polygon
Concave polygon

i15
Polygons in Set A are called convex,
while the polygons in Set B are concave
A polygon is said to be convex if the
lines containing the sides of the polygon
do not cross the interior of the polygon.

i16
Write if the given is convex or concave.

i17
REVIEW
Answer the following:
1. It is a plane formed by three or more segments
such that each segment intersects exactly two
others, one at each endpoint, and no two
segments with a common endpoint are
collinear.
A. Concave C. Polygon
B. Convex D. Shape

i18
Review
2. What do you call the two sides of a polygon that
share a common endpoint?
A. Included side C. Diagonal
B. Included angle D. Consecutive sides

i19
Review
3. What do you call the two sides of a polygon that
share a common endpoint?
A. Included side C. Diagonal
B. Included angle D. Consecutive sides

i20
Review
4. Using the figure, which of the
following is its consecutive
sides?
A. segment AT and segment
TA
B. segment RA and segment
AT
C. segment RT and segment
TR
A
R
T
Polygon 2

i21
Review
5. Using the figure on
the right, what is the
included angle of
segment BC and
segment CD?

i22
Review
included side of
consecutive angles
<ABC and <BAE?

i23
Seatwork
Using the figure on the board, name
a. 6 pairs of consecutive angles
b. 6 pairs of consecutive sides

i24
Seatwork
Using the figure on the board,
c. Name 6 included sides of the consecutive
angles in item a (in order)
d. Name 6 included angles of the
consecutive sides in item b (in order)

i25
REVIEW
1.) It is a kind of polygon whose side/s
crosses the interior part of it. How do you
call it?

i26
REVIEW
included angle of
segment AE and
segment ED?

i27
REVIEW
Tell whether the figure is convex or concave

i28
REVIEW

i29
REVIEW

30
Objectives:
b.) Sides
c.) Angle measurement
Terms

i31
Different Types of Polygons in Convexity
Convex polygon- no line(side) of the polygon
crosses the interior of it
Concave - some of the line(side) crosses the
interior of the polygon

32
Objectives:
a.) convexity
Terms

i33
Activity
MATCHING TYPE
Classify the following base on the number of sides .
Write the letter of your answer. (2 minutes)
1. 3 sides A. PENTAGON
2. 5 side B. TRIANGLE
3. 8 sides C. HEPTAGON
4. 6 sides D. DECAGON
5. 7 sides E. HEXAGON
6. 9 sides F. NONAGO
7. 10 sides G. OCTAGON

i34
REVIEW
1.) It is a kind of polygon with four sides?

i35
REVIEW
2.) It is a kind of polygon with ten sides?

i36
REVIEW
3.) How many dissected triangles can
you form from a 10 sided polygon?

i37
REVIEW
4.) How do we fi d the sum of the interior
angle of a polygon, what is the formula?

i38
REVIEW
5.) Recite the different kinds of polygon
from 3 sides up to 12 sides in order?

i39
Name of
Polygon
Number of
Sides
Name of
Polygon
Number of
sides
Triangle 3 Octagon 8
Quadrilateral 4 Nonagon 9
Pentagon 5 Decagon 10
Hexagon 6 Undecagon 11
Heptagon 7 Dodecagon 12
N-gon n sides
Kinds of Polygons According to Number of Sides

i40
Name of
Polygon
Number of
Sides
Number of
Dissected
triangles
Sum of the
interior
angle
Triangle 3
Quadrilateral 4
Pentagon
Hexagon
Heptagon

i41
Guide Questions
1.) What have you notices on the number
of dissected triangles formed by
diagonals?
2.) How did you get the sum of the
Interior angle of any polygon? What could
be the formula?

i42
105⁰
102⁰
75⁰
95⁰
Example:
Find the measure of <C

i43
Name of
Polygon
Number of Sides
n
Number of
Dissected
triangles
n - 2
Sum of the
interior angle
(n - 2) (180)
Triangle 3
Quadrilateral 4
Pentagon
Hexagon
Heptagon

i44
Answer Checkpoint 2 in page 10

i46
In the convex polygon
ABCDE, A, B, BCD,
D, and E are the interior
angles, while MCD is an
exterior angle.

i48
In the polygon ABCDE, some
consecutive vertices are A and
B, B and C.
Some consecutive sides
Some diagonals are and .
AE and ED; AB and BC
AC and AD .

i49
Different Types of Polygons in terms of
Congruency of Parts
Equilateral polygon if all its sides are equal;
Equiangular polygon if all its angles are
equal;
Regular polygon if it is both equilateral and
equiangular.

POLYGONS.pptx

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POLYGONS.pptx