7. Mr.Santos bought a cartolina
for his Math class. He needs
two triangles of the same size
without wasting any part of the
cartolina. How will he divide it?
What shapes are formed?
8. Look at the illustrations.
1
2
1
2
Suppose we cut a line connecting
two opposite vertices of a rectangle
dividing the figure into two similar
parts.
9. 1
2
1
2
The two similar parts formed from
cutting the rectangle are triangles
which share the common side
(represented by the broken lines)
called the diagonal of the rectangle.
10. A polygon is a closed figure
made up of several line
segments that are joined
together. The line segments
are called sides and do not
cross each other. There are
exactly two sides that meet
at a point.
11. A triangle is a polygon with
3 sides and 3 angles.
A quadrilateral is a
polygon with 4 sides and 4
angles.
12. Look at the illustrations.
60O
60O 60O
The total measure of all the angles
of a triangle is equal to 180 degrees
of interior angles and 360 degrees of
interior angles for a quadrilateral.
15. Mrs. Reyes assigned the Grade 4
class in Math to find out how
quadrilaterals are related to one
another, so she grouped the class
into two.
16. The first group was assigned to
prepare cut-outs of different
quadrilaterals like square,
rhombus, parallelogram, rectangle
and trapezoid. The other group
was assigned to enumerate its
similarities and differences by
writing down the different
properties of each quadrilateral.
17. As the group finished working
cooperatively and collaborately,
they found all the characteristics
of quadrilaterals and relate each
figure to one another. They found
out that both square and rhombus
has 4 equal sides. But a square
has 4 right angles while rhombus
has no right angles.
18. 1. What are the different
quadrilaterals given in the story
problem?
2. In what way is a rhombus
similar to square? In what way it is
different?
3.In what way is a square like a
rectangle? In what way is it
different from rectangle?
19. Let us read some information
on how a quadrilateral is related
to another quadrilateral.
Plane figures with four sides are
called quadrilaterals .
Figure LOVE is a quadrilateral.
L O
V
E
20. Here are the properties of a quadrilateral.
A quadrilateral has four line
segments. The line segment is a
line formed by connecting two
consecutive vertices. A line written
at the top of two letters denotes a
line segment.
Quadrilateral LOVE contains line
Segments LO , OV , VE, and LE.
21. It has four vertices. Vertices are
presented with an upper case
letter of the corresponding vertex
or endpoint. Quadrilateral LOVE
contains vertices which are L, O,
V, and E.
L O
V
E
22. It has four angles. An angle is a
figure formed by two consecutive
sides with a common vertex.
Quadrilateral LOVE contains ∠L,
∠O, ∠V, and ∠E.
E
L O
V
23. It has two pairs of opposite sides.
Quadrilateral LOVE contains LOand
EV which are opposite sides, and LE
and OV which are also opposite.
24. V
E
It has adjacent sides. Adjacent sides are
two lines that meet at a common endpoint
or vertex. They can also be considered
consecutive sides. In Quadrilateral LOVE,
LO and LE have a common vertex, L so LO
and LE are adjacent sides. OL and OV are
also adjacent sides.
25. If exactly one pair of
opposite sides of a
quadrilateral is parallel it is
a trapezoid.The line that at
some point never intersect or
does not meet is called
parallel line.
26. T R
In Quadrilateral PART, PA and
RT do not intersect, that means that
PA and RT are parallel. Therefore,
Figure PART is a trapezoid.
27. If the two nonparallel sides
of a trapezoid are congruent,
it is called an isosceles
trapezoid. In geometry, two
figures or objects are
congruent if and only if they
have the same or equal
measurement.
28. A
N
In trapezoid PLAN, the nonparallel
sides, PN and LA, are the same or
congruent. So quadrilateral PLAN
is an isosceles trapezoid.
29. If two pairs of opposite sides
are parallel, it is a
parallelogram. In a
parallelogram, if the parallel
sides have the same measure
or equal they are considered as
congruent.
30. C
E
A
In quadrilateral CARE, CA is parallel to ER
and CE is parallel to AR . So, Quadrilateral
CARE is a parallelogram.
31. If the angles ofa parallelogram
are right angles, the parallelogram
is a rectangle. In parallelogram
ROLE, RO is parallel to LE and RE is
parallel to OL. ∠R, ∠O, ∠L, and ∠E are
right angles. Thus, parallelogram
ROLE is a rectangle. All the angles in
a rectangle are congruent. In addition,
the parallel sides are congruent; RO
has the same measure or congruent
to LE and REthe same measure to OL.
32. Also, all adjacent sides are
Perpendicular; RO⊥ OL, RO⊥ RE,
LE⊥ OL,LE ⊥ RE. (When all lines
intersect and form a
right angle it is called perpendicular.
We used the symbol ⊥ for
perpendicular.)
E L
O
R
33. S A
E F
A square is a rectangle with all sides are
the same or congruent. Figure SAFE,is a
rectangle with four congruent sides, SA has
the same measure or congruent to AF, AF
has the same measure to FE, and FE has the
same measure to ES. ∠S, ∠A, ∠F, and ∠E
all measures 90° or right angles. Thus, it is
a square.
34. If all the sides of a parallelogram are
congruent, it is a rhombus. See Figure
TAKE, it is a rhombus because the
opposite sides are congruent and all sides
are parallel. In a rhombus, the four angles
need not to be congruent or the same.
E
A
35. If the angles in a rhombus are all right
angles, then the rhombus is a square. In
rhombus JUST, ∠J, ∠U, ∠S, ∠T are right
angles which measures 90°. Hence, it is
also a square. A square may also be
defined as a rhombus in which all angles
are right angles.
T S
U
J
36. Fill in the blanks. Choose your answer
from the box below.
Sides angles polygons
Rectangle square rhombus
180 degrees 360 degrees
parallelogram
1. Triangles and Quadrilaterals are
both called_________.
polygons
37. 2. Triangles and Quadrilaterals
are related according to _________
and__________.
3.Triangles have__________ sum
of interior angles while
quadrilaterals have __________
sum of interior angles.
4. Both pairs of opposite angles are
congruent._________,_______,________,
___________
5.Both pairs of opposite sides are
parallel._________,_________,________,
____________
sides
180 degrees
parallelogram
rhombus
rectangle square
rectangle rhombus
square
parallelogram
360 degrees
38. A. Directions: Answer the following
questions. Write a check (✓) if your
answer is yes, and cross (✖) if it is
no, Write your answers on a
separate sheet of paper.
1. Is any 3-sided polygon a triangle?
2. Is any 4-sided polygon a
quadrilateral?
3. Can a quadrilateral be divided into
two triangles?
39. Direction: Write the letter of the
correct answers on a separate sheet
of paper
1. Which statement proves that a
quadrilateral is a rhombus?
A. There is no line of symmetry.
B. All four sides are congruent.
C. The diagonals bisect each other.
D. The diagonals are perpendicular.
40. 2. Which statement about
quadrilateral is true?
A. All rectangles are always
squares.
B. All trapezoids are always
rhombuses.
C. All rectangles are always
rhombuses.
D. All rectangles are always
parallelogram.
41.
42. References:
A. Books
Ang, Erlinda, Bayle, Ma. Teresa, Cruz,
Gloria, 2007. Grade School
Mathematics 4. Quezon City: Rex
Printing Company, Inc.
Deauna, Melecio C. & Deauna, Florita C.
Lamayo, 2011. Let’s Do Math 4. Sta.
Cruz Manila: Saint Mary’s Publishing
Corporation
43. References:
B. Electronic Resources
Deped Commons “K to 12 MELCS with
CG Codes” Accessed January 4,
2021.https://commons.deped.gov.p
h/K-to- 12-MELCS-with-CG-
Codes.pdf
“ Math – Elements of Quadrilaterals –
Sides and Diagonals – English “
https://youtu.be/8gAnoPilk8
44. Mathematics 4 Video Production Team
Genalyn O. Bautista
Talent/ Script Writer/ Powerpoint Maker
Lanie F. Santiago
Content Editor
Eliza P. Dioses
Video Editor
Alfonso B. De Guzman Jr. PhD
Director
45. SDO – San Jose City
Management Team
Johanna N. Gervacio, PhD, CESO VI
OIC – Schools Division Superintendent
Veronica B. Paraguison, PhD
CID Chief
Sierma R. Corpuz
Division ADM Coordinator/ EPS in Math
