Mathematics III

(Effective Alternative Secondary Education)

MATHEMATICS III

MODULE 3Geometry of Shape & Size-

Quadrilaterals

BUREAU OF SECONDARY EDUCATION

Department of Education

DepEd Complex, Meralco Avenue, Pasig City

Module 3

Quadrilaterals

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 and ability to appreciate their application in daily life. Treat the lesson with fun and take time to go back if you think you are at a loss.

What you are expected to learn

This module is designed for you to learn

1. illustrate a Quadrilateral and 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

O

1. Quadrilateral ZENY is a ____.

a. parallelogramb. trapezoidc. trapeziumd. rectangle

2. A diagonal of quadrilateral ZENY is ____.

a.

b.

c.

d.

3.

is opposite angle ____.

a.

b.

c.

d.

4.

& are the ____ of the Quadrilateral DETH

a. medianb. altitudec. basesd. legs

5.If then BETH is a/an ____.

a. rectangle

b. trapezium

c. isosceles trapezoid

d. square

6.

are the _____ of Quadrilateral BETH.

a. legs

b. bases c. median d. altitude

7. whish is the median of quadrilateral DETH

a.

b.

c.

d.

8. What kind of parallelogram is quadrilateral DETH?

a. rhombusb. squarec. parallelogramd. rectangle

9. Using the figure at the right which is a rhombus?

a. ACGHb. CEFG

c. BDGHd. AEFH A B C D E

HGF

10. Which is a rhombus and a rectangle?

a. AEFHb. CEFGc. ACGHd. BDGH

What you will do

Lesson 1

Identifying and Naming Quadrilaterals.

A quadrilateral is a polygon of four sides

Example:

M O D E O

O L

AD E R P M E

You ca name a quadrilateral by its vertices. The order of vertives is very important. You read or write the four letters clockwise or counterclockwise.

Examples: R O

You can name a quadrilateral at the

Right as.

ROSE or OSER or SERO or EROS

Or RESO or ESOR or SORE

ES

The name of this quadrilateral can be: K L

KLMN or LMNK or MNKL or NKLM

Or NMLK or MLKN or LKNM or KNML

N M

Try this out.

A. Which of the following is a quadrilateral or not.

1) 3) 5)

2)

4)

6)

7) 9)

8) 10)

B. Name the following quadrilaterals.

C

1) O

2) H O

D L E P

3)B E

4) O P

H A T S

5)A

L R

6) B M

A

Y Y

7)MA8)A B

YN D

C

9) OR

10)

S

P R

Q

S E

C. Name & Identify the Quadrilaterals in the figure.

A B

C

D

EEE hhhdhjhsjsjj

Name 10 Quadrilaterals.

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: , , ,

the vertices are: L, O, V, E

the angles are , , ,

the diagonals are &

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 and are consecutive sides. So, and , and , and are other pairs of consecutive sides. On the otherhand, and , and are opposite sides.

Two angles with a common side like and are consecutive angles, the others are and , and , and , on the other hand, and ; and are opposite angles.

Try this out

A. Using quadrilateral COLA, identify1. two pairs of opposite vertices

2. two pairs of opposite angles

3. two pairs of opposite sides

4. one pair of diagonals

5. four pairs of consecutive vertices

6. four pairs of consecutive angles

7. four pairs of consecutive sides

8. four sides of quadrilateral POEM

9. four angles of quadrilateral POEM

10. two diagonals that can be drawn in quadrilateral POEM

B. Fill the blanks:

1) ______ the vertex opposite S

2) ______ is the opposite side of

3) is opposite _________

4) and are _______ sides.

5) The diagonals that can be drawn are and ______

6) and are ___________ sides.

7) B and C are consecutive vertices, B and _____ are also consecutive vertices.

8) and _____ are the diagonals of quadrilateral ABCD.

9) and are ______ angles.

10) and _____ are opposite angles.

C.Choose the letter of the correct answer. Use quadrilateral D E T H

1. How many diagonals has quadrilateral DETH?

a. oneb. twoc. threed. four

2. The sides of quadrilateral DETH are

, , and ______

a.

b.

c.

d.

3. is opposite of what angle?

a.

b.

c.

d.

4. The opposite side of is _________

a.

b.

c.

d.

5. The diagonals of quadrilateral DETH are _________

a. &

b. &

c. &

d. &

Given: quadrilateral PQRS

6. How many vertices are there in

Quadrilateral PQRS?

a. oneb. twoc. threed. four

7. A pair of consecutive sides is and ______

a.

b.

c.

d.

8. A pair of opposite vertices is P and ______

a. R

b. Q

c. S

d. M

9. How many pairs of opposite has quadrilateral PQRS?

a. oneb. twoc. threed. four

10. How many pairs of consecutive sides has quadrilateral PQRS?

a. oneb. twoc. threed. fourLesson 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 linestwo lines are parallel if they are coplanar and they do not meet.

ii. perpendicular linestwo lines are perpendicular if they intersect and form a right angle.

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 intersects at O and is a right angle, then is perpendicular to , in symbol:

4,If is a right angle, then

Try this out.

A.Which of the following seem to be parallel?

Write yes if it is and no if not.

1)

7)

2)

8)

3)

9)

4)

10)

5)

6)

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.

2)Two intersecting lines which form a right angle.

3)

4)

5)

6)

7)

8)

9)

10)

Lesson 4Kinds 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 , then HOPE is a trapezoid.

3.Parallelogram

If a quadrilateral has two pairs of parallel sides, then it is a parallelogram.

If and then STOP is a parallelogram.

A.Identify:

______ 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

______ 9.Quadrilateral PEAK

______ 10.Quadrilateral LOAF

B.Select the correct word from the set (trapezium, trapezoid, parallelogram)

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

5.trapezoid with diagonals

Two tents are fixed above. Give me:

6.

7.three parallelograms

8.

9.

10.

O

L

E

V

C

O

L

A

P

O

E

M

Q

P

R

S

B

C

D

A

E

D

O

I

H

R

Q

P

S

Quadrilateral

Trapezium

Parallelogram

Trapezoid

B

A

D

C

X

O

Y

R

S

L2

L1

M

A

N

L

K

J

I

F

G

C

H

E

A

D

B

Q

V

P

U

T

R

S

Y

D

O

B

Two trapezoids

A

E

D

F

B

C

H

Gx

J

H

K

L

N

M

A

N

Dx

Sx

Hx

Tx

Yx

Hx

Gx

Fx

Ex

Ux

Vx

Rx

Px

Wx

Cx

Lx

Ox

Mx

R

Q

K

J

O

K

M

E

X

R

E

X

S

A

T

O

X

A

F

L

A

E

M

E

X

R

E

X

S

A

T

O

X

P

X

X

R

E

X

S

A

T

O

X

P

E

C

O

L

D

S

O

X

X

C

O

L

D

X

X

X

N

E

W

H

O

P

T

S

E

P

H

O

E

M

R

D

Y

X

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