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What are the relationship among the

lengths of the sides of rectangle

ABCD on the right?

Because all sides of a rectangle are equal, then it iscalled a square.

Now try to find square objects around you.

What are you going tolearn? To define a square

To d iscover the fo rmula

of the perime ter and

area o f a squa re

Key Terms square

8.2

Do this with your partner

Materials: paper, scissors, a ruler and a protractor

1. Draw rectangle ABCDwith AB=BC=CD=AD=5 cmas shown in the figure on the right.

2. Draw the diagonals of the rectangle ABCDandmark the intersection of the diagonals, then name itpoint O.

3. Use a protractor to measure the angles below.AOB=....... BOC=....... COD=.......

DOA =....... OAD=....... OBA =.......

OCB=....... ODC=....... OAB=.......

OBC=....... OCD=....... ODA =.......

4. What are the measures of AOB, BOC, COD, and DOA?

5. What are the measures of OAD, OBA, OCB, and ODC?

6. What are the measures of OAB, OBC, OCD, and ODA?

7. Based on the above activity, what can you conclude? Explain it.

D

B

C

O

A

Mini - Lab

PROBLEM 7 D

B

C

O

A

Critical Thinking 1. What are the measures of BACand BCA?2. What are the measures of DBA and ADB?

PROBLEM 8

Mathematics for Junior High School Year 7 /311

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The properties of a square:

1. The opposite sides are parallel.

2. All of the angles are right angles.3. The diagonals are equal and bisect each other.

4. All the sides are equal.

5. The diagonals bisect the angles.

6. The diagonals cross perpendicularly.

Based on those properties, we can say that a square is a

rectangle with 4 equal sides.

PROBLEM 9 Are all properties of a rectangle also owned by asquare? Explain. Can it be in the vice versa?

PROBLEM 10The figure on the left is square PQRS.

a. List 3 segments equal to PQ .R

O

S

Q

b. List 3 segments equal to OP .c. List all right angles in square PQRS.

P

D C

B

What are the perimeter and area of

the squareABCD? Explain.

Given a square that has the length of the side ofs. IfP is the

perimeter and A is the area, then the formula of perimeter and area of

the square is P = 4s and A = s s.

A

s

s

PROBLEM 11

/ Students Book Quadrilaterals312

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Related to the Real World

S

t

r

ee

t

House

Banana

Field

23 m

23 m23 m

30 m

PROBLEM 12

Calculate the perimeter and area of the land used for

a. the house b. the banana field

PROBLEM 13 A square has the perimeter of 32 cm.Calculate the area of the square.

Try This Calculate the area of a square having the

perimeter of 8 m.


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1. Determine whether the following statements are T or F (True

or False). Give your reasons.a.Each angle in a square is a right angle.

b.Each angle in a rectangle is a right angle.

c.The lengths of the four sides of a rectangle are equal.

d.The lengths of the diagonals of a square are equal.

e.The lengths of the four sides of a square are equal.

f. The diagonals of a rectangle bisect the angles into two

equal parts.

g.The diagonals of a square bisect the angles into two equalparts.

h.The diagonals of a square bisect each other and form right

angles.

i. The set of all squares is the subset of the set of all

rectangles.

2.

Suppose KLMNis a square and OK= 3 cm, thena. OL = ...... = ...... =...... = ...... cm.

b. KM= ...... = ...... cm

c. KOL = ........ = ........ = ........ = .......

d. OKL = ......... = .....

e. OLK= ........ = .....

f. OML = ........ = .....

g. ONM= ....... = .....

3. Let UVWXbe a square, then

a. Because 3x7= ............, then x=..............

b. VX= .......

c. The length of the side of square

UVWXis .........

4. In square KLMNon the left, the

length ofON

is 5 cm.a. What are the lengths of OK , OL , and OM ?

K

L

O

N

M

O

3 cm

L

N

K

M

X

U

V2x+5

3x7W


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b. What are the lengths of KM and LN ?

BA

CD

8 cm

5. Let ABCD be a square.

a. Name two pairs of parallel lines.

b. Name four lines which have exactlythe same length.

c. Name two lines which have exactly

the same length.

d. What is the length of all sides of square ABCD?

6. Open Question. Name at least five objects around

you with a square shape.

7. Drawing. Draw square PQRS whose diagonals intersect atpoint O. The length of diagonal QS is 7 cm and draw diagonal

PR horizontally. Find the length of the sides of square PQRS

using a ruler.

8. Drawing. Draw the diagonals of the following squares.

S

PR

Q U

Y

V

X

E F

H G

a. Fill in the blanks.

EG = ..... ; PR = ..... ; and VY= ......

b. Name all pairs of parallel lines on each square.

c. Name all equal lines on each square.

d. Suppose point O is the intersection of the diagonals,name all right angles on each square.

9. Critical Thinking. What can you

conclude about the sum of the measure of

all angles of a square?D

A

C

O

B

10. Look at squareABCD on the right.

a. If AC= 5x19 and BD = 3x+7, find the

lengths of the diagonals.


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b. If AD = 4y15 and AB = y+6, find the

lengths of all sides.

11.Open Question. Adi has a wire of 20 cm in length. He

wants to make some squares and rectangles. How manysquares and rectangles can be made?

12.Name some common properties of a rectangle and a square.

13.Name the properties of a square which a rectangle does not

have.

14.Does a square have exactly the same properties as a

rectangle?

15.Complete the following table.

No. Length of

side

Perimeter of the

square

Area of the

square

a. 11 cm .......... cm ........ cm2

b. 15 cm .......... cm ........ cm2

c. ...... m 36 m ........ m2

d. ...... m 84 m ........ m2

e. ...... km ........ km 49 km2

f. ...... km ........ km 25 km2

16.Calculate the perimeter and area of the following

rectangles and squares.

a. b. c. d.

9 cm

5 cm

6 cm

6 cm

3 cm

10 cm

7 cm

7 cm

17.Calculate the perimeter and area of a square having the

following length of sides.

a. 2.5 m. b. 14 cm. c. 21 dm.


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18.Calculate the perimeter and area of the figure below.

10 cm

3 cm

4 cm

4 cm

3 cm

2 cm

3 cm

19.In a square garden having 10 m sides, there is a

rectangular swimming pool which is 8 m long and 6 m

wide. What is the area of the land in the garden in

which flowers can be planted?

20.The area of a square is 64 cm2. Calculate the perimeter.

21.Calculate the length of the sides and the perimeter of a

square having the area of:

a. 144 cm2 b. 625 m2

22.Critical Thinking. The lengths of the sides of a new

square are 3 times longer than the original. What is the

ratio between the original area of the square and thenew one?

23.Calculate the area of the shaded area in the following.

a. b.

4 cm

4 cm

2 cm

6 cm

6 cm

2 cm

2 cm

10 cm

2 cm

5 cm4 cm

3 cm

3 cm

3 cm

2 cm

24.Is it possible to draw a square and a rectangle that havethe same area but different perimeter? Explain youranswer.

25.Is it possible to draw a square and a rectangle that have

the same perimeter but different area? Explain youranswer.


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26.Can you calculate the perimeter of a square if the area isgiven? Explain your answer.


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