Module 3
Geometry of Shape and Size
What this module is about
This module is about Quadrilaterals. As you go over the
exercises, you will develop skills in identifying Quadrilaterals and their
parts. You will learn to appreciate the lesson as they are applied in
your daily life.
What you are expected to learn
This module is designed for you to learn to: 1. identify a Quadrilateral and name its parts 2. illustrate the different kinds of Quadrilaterals
How much do you know
Write the letter of the correct answer
Z E
Y N 1. Quadrilateral ZENY is a ____.
a. parallelogram b. trapezoid c. trapezium d. rectangle
2. A diagonal of quadrilateral ZENY is ____. a. ZE b. ZN c. ZO d. ZY
3. Y is opposite angle ____.
Using the figure below:
D B E
M P
H T
4. DH & ET are the ____ of the Quadrilateral DETH a. median b. altitude c. bases d. legs
5. If BHET then BETH is a/an ____. a. rectangle b. trapezium c. isosceles trapezoid d. square
6. BH ET are the _____ of Quadrilateral BETH.
a. legs b. bases c. median d. altitude
7. Which is the median of quadrilateral DETH? a. BH b. MP c. EA d. DH
8. What kind of parallelogram is quadrilateral DETH?
a. rhombus b. square c. parallelogram d. trapezoid
9. Using the figure below, which is a rhombus? a. ACGH b. CEFG
c. BDGH d. AEFH
A B C D E
H G F
10. Which is a rhombus and a rectangle?
What you will do
Lesson 1
Identifying and Naming Quadrilaterals.
A quadrilateral is a polygon of four sides
Examples:
R
M O D E O O L
V
A D E R P M E
You can name a quadrilateral by its vertices. The order of vertices is very important. You read or write the four letters clockwise or counterclockwise.
Examples:
You can name a quadrilateral the right as:
ROSE or OSER or SERO or EROS Or RESO or ESOR or SORE
The name of this quadrilateral can be:
KLMN or LMNK or MNKL or NKLM Or NMLK or MLKN or LKNM or KNML
Try this out
A. Which of the following is a quadrilateral?
1) 3) 5)
R O
E S
K L
2) 4) 6)
7) 9)
8) 10)
B. Name the following quadrilaterals.
1. 2.
C
O H O
D L E P
3. 4.
B E O P
H A T S
5. 6. A
B M
L R
A
7. M A 8. A B
Y N D C
9. 10. S O R
P R
S E Q
C. Identify an name 10 quadrilaterals in the figure:
A B C D
EEE hhhdhjhsjsjj
S F
T
U
V
W O
K I
N M
R Q
P S
Y
Lesson 2
Parts of a Quadrilateral
A quadrilateral has the following parts:
4 sides 4 vertices 4 angles 2 diagonals
You can take a look on quadrilateral LOVE
the sides are: LO, OV, EV , LE
the vertices are: L, O, V, E
the angles are L, O, V , E
the diagonals are LV & OE
diagonals are segments joining opposite vertices.
The vertices E and O; L and V are opposite vertices. Vertices L and O, O and V, V and E, E and L are consecutive vertices.
Two sides with a common vertex like LO and OV are consecutive sides. So, OV and VE, VE and EL, EL and LO are other pairs of consecutive sides. On the otherhand, LO and EV , OV and LE are opposite sides.
Two angles with a common side like L and O are consecutive angles, the others are O and V , V and E, E and L, on the other hand, E
and O; L and V are opposite angles.
Try this out
A. Using quadrilateral COLA, identify:
1. two pairs of opposite vertices
2. two pairs of opposite angles
3. two pairs of opposite sides
L O
E V
6. four pairs of consecutive angles
7. four pairs of consecutive sides
Using the figure at the right:
8. four sides of quadrilateral POEM
9. four angles of quadrilateral POEM
10. two diagonals that can be drawn in quadrilateral POEM
Refer to the figure at the right. Fill the blanks:
1. ______ the vertex opposite S
2. ______ is the opposite side of PS
3. Q is opposite _________
4. PQ and QR are _______ sides.
5. The diagonals that can be drawn are QS and ____.
Given the figure:
6. BC and CD are ___________ sides.
7. B and C are consecutive vertices, B and _____ are also consecutive vertices.
8. AC and _____ are the diagonals of quadrilateral ABCD.
9. A and D are ______ angles. 10. A and _____ are opposite angles.
E M
P O
A D
C B
R S
C. Choose the letter of the correct answer. Use quadrilateral D E T H
1. How many diagonals has quadrilateral DETH? a. one b. two c. three d. four
2. The sides of quadrilateral DETH are
DH, HT, TE and ______
a. HE b. DT c. DE d. DO
3. LH is opposite of what angle?
a. E b. D c. T d. O
4. The opposite side of ET is _________ a. DO b. DE c. HT d. DH
5. The diagonals of quadrilateral DETH are _________
a. DO & OT b. HE & DT c. DH & ET d. DE & HT
Given: quadrilateral PQRS
6. How many vertices are there in Quadrilateral PQRS?
a. one b. two c. three d. four
7. A pair of consecutive sides is PQ and ______ a. QR b. RS c. PR d. QS
8. A pair of opposite vertices is P and ______
a. R b. Q c. S d. M
9. How many pairs of opposite s has quadrilateral PQRS? a. one b. two c. three d. four
10. How many pairs of consecutive sides has quadrilateral PQRS? a. one b. two c. three d. four
E D
O
H I
Q R
Quadrilateral
Trapezium Trapezoid Parallelogram
Lesson 3
Parallels & Perpendiculars
Kinds of Quadrilaterals:
As you can see the diagram of the different kinds of quadrilaterals, you can notice the characteristics of the sides of each quadrilateral.
Before you proceed to the definition of each quadrilateral, you must know first the meaning of the following:
i. parallel lines two lines are parallel if they are coplanar and they do not meet.
Examples:
1. two lines are parallel if they are coplanar and they do not meet.
2. l1 is parallel to l2. In symbol l1 // l2
3. If XY intersects RS at O and XOS is a right angle, then XY is perpendicular to RS, in symbol: XY RS
4. If MAN is a right angle, then AN
AM
C
A
B
D
L
1L
2X
S
R
Y
O
Try this out
A. Which of the following seem to be parallel? Write yes if it is and no if not.
1. 6.
2. 7.
3. 8.
4. 9.
B. Write parallel or perpendicular.
1. 4.
2.
5.
3.
6. A pair of lines of your pad paper
7. The corner of the blackboard
8. Railroad tracks
9. The grills
10. A pair of consecutive sides of a picture frame
C. Are we parallel or perpendicular?
1. Two lines on a plane which do not meet.
P V Q
R S
3.
4. AB&BD
5. FG&EH
6. KI &FG
7. PT &TU
8. QR&PS
9. PV &TU
10. BY &BO
K L
I J G F
E H
A
B
C
D
U T
B O
Lesson 4
Kinds of Quadrilaterals
1. Trapezium
If a quadrilateral has no parallel sides, then it is a trapezium. MORE is a trapezium.
2. Trapezoid
If a quadrilateral has exactly a pair of parallel sides, then it is a trapezoid. If HO// EP, then HOPE is a trapezoid.
3. Parallelogram
If a quadrilateral has two pairs of parallel sides, then it is a parallelogram. If ST // PO and SP// PO then STOP is a parallelogram.
D R
E M
H O
P E
O
T S
Try this out
A. Identify the kind of quadrilateral:
1. A quadrilateral whose opposite sides are parallel. 2. A quadrilateral with no parallel sides.
3. A quadrilateral with a pair of parallel sides.
4. Quadrilateral WHEN.
5. Quadrilateral COLD.
6. Quadrilateral SORE
7. Quadrilateral PEAS
8. Quadrilateral TOME
W H
N
E
C
L
O
D
X X
X
X
S O
R E
X
X
P
S
E
A
M
E X
T X O
9. Quadrilateral PEAK
10. Quadrilateral LOAF
B. Select the correct word from the set (trapezium, trapezoid, parallelogram)
G E
A N
D
x S
x H x T x Y x H x F x U x V x R x P x W x C x L
x O
x M
x R
Q K
J
P E
A K
L
O
A
1. quadrilateral DETH 2. quadrilateral DANS 3. quadrilateral SNLU 4. quadrilateral LOVU 5. quadrilateral JMRK 6. quadrilateral OMPV 7. quadrilateral RWCR 8. quadrilateral WGFC 9. quadrilateral PWGY 10. quadrilateral TERY
C. Draw the following figures:
1. trapezium ZENY 2. trapezoid BETH 3. parallelogram LOVE
4. parallelogram with diagonals DL&BW
5. trapezoid with diagonals IE&MC
Two tents are fixed below:
Give me:
6.
7. three parallelograms 8.
9. 10.
A
E
D
F B
C H
G x
J H
K L
N
Lesson 5
TRAPEZOIDS
Trapezoid
Isosceles Trapezoid
Parts of a Trapezoid
Aside from the vertices, angles, sides and diagonals of a trapezoid, a trapezoid has the bases, the base angles, the legs, the median and the altitude.
In quadrilateral BETH, BE// HT, then BETH is a trapezoid.
The bases are the parallel sides BE and AT are the bases.
The base angles are the angles including either base.
H
and T are the bases.
The legs are the non parallel sides.
BH and ET are the legs.
The median of a trapezoid is a segment
joining the midpoints of the non-parallel sides. MO is the median of trapezoid BETH
The altitude of a trapezoid is the segment included between the bases and perpendicular to either one of them.
EP is the altitude of trapezoid BETH.
Special Kind of a Trapezoid
A special kind of a trapezoid is the isosceles trapezoid.
An isosceles trapezoid is a
trapezoid whose legs are congruent.
If ZY EN then ZENY is an Isosceles trapezoid.
O B
M
H
E
T
Z
Y N
Try this out
A. Match Column A with Column B.
Column A Column B
1. quadrilateral STAR a. consecutive sides
2. quadrilateral STIR b. trapezoid
3. TI c. legs
4. RA&ST d. base angles
5. ST &SR e. midpoint
6. SA f. altitude
7. BP g. bases
8. SR& AT h. median
9. R&STA i. Opposite angles
10. R&RAT j. parallelogram
k. diagonal B. Identify
1. A quadrilateral with a pair of parallel sides.
2. The segment joining the midpoints of the legs of a trapezoid.
3. The non-parallel sides of a trapezoid.
I S
B
R
T
P
6. A pair of sides with a common vertex.
7. Two angles whose vertices are the endpoints of a side.
8. Trapezoid with equal non parallel sides.
9. A segment from a side to the opposite side.
10. A polygon of four sides.
C. Use the figure to identify:
1. X of AD
2. AM of quadrilateral DATE
3. Quadrilateral DATE if ADTE
4. AD and TE of quadrilateral DATE
5. DE of quadrilateral DATE
6. XY of quadrilateral DATE
7. Quadrilateral ATPM
8. D of quadrilateral DATE
9. AT and DE
10. AE X
D
A T
Y
E P
Lesson 6
Parallelogram
Parts of a Parallelogram
In a parallelogram, you have also the bases and the altitudes.
The bases of a parallelogram are either pair of opposite sides.
The altitude is a segment included between the bases and perpendicular to either one of them.
AD or BC is a base and ET is the altitude to either base. Parallelogram
Square
Rectangle Rhombus
B
A
E C
T D
Kinds of Parallelogram
There are three kinds of parallelogram. You have the rectangle, the rhombus and the square.
A rectangle is a parallelogram with a right angle. PURA is a rectangle.
A rhombus is a parallelogram with a pair of congruent consecutive sides.
SONY is a rhombus.
A square is a parallelogram with a right angle and a pair of congruent consecutive sides.
So, if you take a square with a right angle, it is a rectangle with a pair of congruent consecutive sides, if you take a square with a pair of congruent consecutive sides, it is a rhombus with a right angle.
BOSE is a square.
A. Identify:
1. A polygon of four sides.
2. A quadrilateral with two pairs of parallel sides.
3. A segment included between the bases and perpendicular to either one of them.
4. Either pair of opposite sides of a parallelogram.
5. A segment joining any 2 opposite vertices.
6. A parallelogram with a right angle.
7. A parallelogram with a pair of consecutive sides congruent. S
Y
O
N
P U
A R
B O
8. A rhombus with a right angle.
9. A rectangle with a pair of consecutive sides equal
10. A quadrilateral with four equal sides.
B. Classify each statement as true or false.
1. Every parallelogram is a quadrilateral.
2. Every quadrilateral is a parallelogram.
3. If quadrilateral PONY is a parallelogram then PO //YN .
4. There exists a parallelogram with all sides congruent.
5. There exists a parallelogram with all angles congruent.
6. There exists a parallelogram ABCD where AB// AD 7. CL is a diagonal of parallelogram COLD.
8. There exists a parallelogram that is not a plane figure.
9. A square is a rectangle.
10. A rhombus is a square.
C. Write the letter which corresponds to those given in the figure or parts of the figures below.
1. rectangle 6. base
2. parallelogram 7. isosceles trapezoid A
w
B
r
x
C
y
D
E
v
F
t s
o
G m
Let’s Summarize
A quadrilateral is a polygon of four sides.
The parts of a quadrilateral are the vertices, the angles, the sides and the diagonals.
A quadrilateral can be named by its vertices.
The kinds of quadrilateral can be summarized by drawing the Family Tree of Quadrilaterals.
four sided polygon Quadrilateral
Trapezium
No parallel sides
Trapezoid parallelogram
With a pair of parallel sides
With 2 pairs of parallel sides
isosceles
square With a right
angle With a pair of
consecutive sides congruent
With a right angle and with a pair of consecutive sides
congruent
Two lines are parallel if they are coplanar and do not meet.
Perpendicular lines are intersecting lines which form a right angle.
In a trapezoid, the non-parallel sides are the legs, the parallel sides are the bases.
Base angles of a trapezoid are the two angles including a base. The median is a segment joining the midpoints of the non-parallel sides of a trapezoid. The altitude is the segment included between the bases and perpendicular to either one of them.
In a parallelogram, the bases are either pair of opposite sides. The altitude is a segment included between the bases and perpendicular to one of them.
What have you learned
A
O K R
M
S C E
W Q P
Identify by matching Column A with Column B. Write only the letter.
Column A Column B
1. MOR&REM a. quadrilateral
2. quadrilateral MORE b. opposite angles
3. AC c. consecutive vertices
4. CE &QP d. parallelogram
5. CQ&EP e. trapezium
6. quadrilateral CEPQ f. square
7. XY g. rhombus
8. quadrilateral WSCQ h. altitude
9. quadrilateral CAKE i. Bases
10. S & W j. kgs
k. isosceles trapezoid
Answer Key
How much do you know
1. a 6. a
2. b 7. b
3. b 8. d
4. d 9. c
5. c 10. b
Try this out
Lesson 1
A. 1. quadrilateral B. 1. DLDC, LOGD, OCDL, DLOC 2. not COLD, OLDC, LDCO, DCOL 3. quadrilateral 2. BEAH
4. not 3. LARY
5. quadrilateral 4. MANY 6. quadrilateral 5. SERO 7. quadrilateral 6. HOPE 8. quadrilateral 7. STOP 9. quadrilateral 8. BAMY
10. not 9. ABCD
10. PQRS
(Answers may vary)
C. 1. ADWP 2. LVWP 3. OKUV 4. MITV 5. IFST 6. FCDS 7. MHCF 8. GYCB 9. LNRP 10. MNRQ
(Answers may be in any order)
Lesson 2
A. 1. C & L, A & O B. 1. Q C. 1. b
5. C & O, O & L 5. PR 5. b L & A, A & C 6. consecutive 6. d 6. C&O,O&L 7. A 7. a
C A A
L
& , & 8. BD 8. a
7. AC &CO,CO&OL 9. consecutive 9. b
AC LA LA
OL& , & 10. C 10. d 8. PO,OR,EM &MP
9. P,O,E&M
10. PE &MO
Lesson 3
A. 1. yes B. 1. parallel C.1. parallel
2. yes 2. perpendicular 2. perpendicular 3. no 3. perpendicular 3. perpendicular 4. no 4. parallel 4. perpendicular 5. yes 5. parallel 5. parallel
6. no 6. parallel 6. perpendicular 7. no 7. perpendicular 7. perpendicular 8. no 8. parallel 8. parallel
9. yes 9. parallel 9. parallel
10. no 10. perpendicular 10. perpendicular
Lesson 4
A. 1. parallelogram B. 1. parallelogram C.1-5. may vary 2. trapezium 2. trapezium 6. ABCD 3. trapezoid 3. trapezoid 7. GKLS 4. trapezium 4. parallelogram 8. JLMH 5. parallelogram 5. trapezoid 9. FBDC 6. trapezoid 6. trapezium 10. JHMN 7. parallelogram 7. parallelogram
8. parallelogram 8. trapezoid 9. trapezoid 9. trapezoid 10. trapezium 10. parallelogram
Lesson 5
6. k 6. consecutive sides 5. base 7. h 7. consecutive angles 6. median 8. c 8. isosceles trapezoid 7. parallelogram 9. I 9. altitude 8. base angle 10. d 10. quadrilateral 9. parallel sides or
bases 10. diagonal
Lesson 6
A. 1. quadrilateral B. 1. true C. 1. B 2. parallelogram 2. false 2. C 3. altitude 3. true 3. F
4. bases 4. true 4. D
5. diagonal 5. true 5. E
6. rectangle 6. false 6. r, t, n, m
7. rhombus 7. true 7. G
8. square 8. false 8. v, s, x
9. square 9. true 9. w
10. rhombus & square 10. false 10 o
