The document provides an introduction to quadrilaterals, defining them as polygons with four sides and describing their types, including parallelograms, rectangles, rhombuses, squares, trapezoids, isosceles trapezoids, and trapeziums. It explains key concepts such as vertices, sides, angles, and diagonals, as well as the properties that distinguish each type of quadrilateral. The material emphasizes the geometric relationships and classifications of quadrilaterals, suitable for learning mathematics.

1. Hello everyone!
Learn to Love,
Love to Learn

2. MATHEMATICS
9
Quarter 3:
Module 1
Part 1
QUADRILATERALS

3. QUADRILATERAL
Quadrilateral is a
polygon with four
sides.
A
B
C
D

4. Quadrilaterals
Around You

5. • A quadrilateral is named
by its consecutive sides.
• In the figure, the
quadrilateral is named
ABCD or BCDA or
CDAB or DABC.
A
B
C
D

6. • The quadrilateral has four
vertices namely A, B, C, and D.
• Vertices A and B, B and C, C and
D, and D and A are called
consecutive vertices.
• Vertices A and B, and C and D
are called opposite vertices.
A
B
C
D

7. • Two sides with a common
vertex, like 𝐴𝐵 and 𝐵𝐶, are
adjacent sides.
• On the other hand, 𝐴𝐵 and
𝐷𝐶 are opposite sides.
A
B
C
D

8. • Two angles with a common
side, like ∠A and ∠B, are
adjacent angles.
• On the other hand, ∠B and
∠D are opposite angles.
A
B
C
D

9. • Segments joining
opposite vertices, like
𝐴𝐶, is called diagonal
of the quadrilateral.
A
B
C
D

10.  The diagonals of a convex quadrilateral are contained entirely
inside of the figure.
 While in concave quadrilateral, one of the diagonal lie outside
the figure.
A
B
C
D
Convex Quadrilateral
E
H
F
G
Concave Quadrilateral

11. • Diagonals 𝐴𝐵 and 𝐵𝐶 of quadrilateral ABCD intersect.
• Diagonals 𝐴𝐵 and 𝐵𝐶 of quadrilateral EFGH do not intersect
A
B
C
D
Convex Quadrilateral
E
H
F
G
Concave Quadrilateral

12. KINDS
OF
QUADRILATERALS

13. Parallelogram
• It is a quadrilateral with two
pairs of parallel sides.
• ABCD is a parallelogram
with 𝐴𝐵║𝐷𝐶 and 𝐵𝐶║𝐴𝐷.

14. Note:
Right angles measures 90ᴼ.
E F
G
H
Rectangle
• It is a parallelogram with
four right angles.
• EFGH is a rectangle with
∠E, ∠F, ∠G, and ∠H that are
right angles.

15. Rhombus
• It is a parallelogram with four
congruent sides.
• MNOP is a rhombus with
MN ≅ NO ≅ OP ≅ PM.
M
P O
N

16. Square
• It is a rectangle with four
congruent sides.
• IJKL is a square with
ഥ
IJ ≅ ഥ
JK ≅ KL ≅ ഥ
LI, and ∠I, ∠J,
∠K, and ∠L are right angles.
J K
L
I
Note:
A square is both a rectangle
and a rhombus.

17. Trapezoid
• It is a quadrilateral with exactly one
pair of parallel side.
• QRST is a trapezoid with QR║TS. The
parallel sides are called the bases, and
the non-parallel sides are called the
legs.
• The angles on the bases of the
trapezoid are called base angles.
T
Q R
S
 The sides QR and TS are the
bases, and TQ and SR are the
legs. On the other hand, ∠T
and ∠S are called base angles,
and so are ∠Q and ∠R.

18. Isosceles Trapezoid
• It is a trapezoid with legs are
congruent.
• WXYZ is an isosceles
trapezoid with WX ≅ ZY.
X
W Z
Y

19. Trapezium
• It is a quadrilateral with no
parallel sides.
• ABCD is a trapezium.
A
B
C
D

20. THANK
YOU
HAVE A NICE
DAY!
I
MATh