Construction of Square

Q. Ajay is constructing a square PQRS with PQ = 5 cm. The steps of construction are as follows.

(i) Draw a line segment PQ of length 5 cm. Construct 90° at the points P and Q. Extend the rays from P and Q.
(ii) Draw arcs of radius 5 cm keeping P and Q as centre on the extended rays.
(iii) Mark the intersecting points to be S and R.
Which of the following figure represents the completion of the construction of above mentioned steps?

1. 
2. 
3. 
4. 

Q. Construct a square ABCD, each of whose diagonals is 5.2 cm.

Q. Construct a square in which each diagonal is 5 cm long.

Q.

Question 94

Solve the following question:

Can a right-angled triangle with sides 6 cm, 10 cm and 8 cm be formed? Give reason.

Q.

Is it possible to construct a square if only one of its diagonal is given?

1. With 4 other measurement, Yes

2. With measurement of a side, Yes

3. Yes

4. No

Q. Construct a square of diagonal AC =6.2 cm.

Q.

Question 1
Construct the square READ with RE = 5.1 cm.

Q. Ajay is constructing a square PQRS with PQ = 5 cm. The steps of construction are as follows.

(i) Draw a line segment PQ of length 5 cm. Construct 90° at the points P and Q. Extend the rays from P and Q.
(ii) Draw arcs of radius 5 cm keeping P and Q as centre on the extended rays.
(iii) Mark the intersecting points to be S and R.
Which of the following figure represents the completion of the construction of above mentioned steps?

1. 
2. 
3. 
4. 

Q. Construct a parallelogram ABCD, when: Diagonal AC = 6.4 cm, diagonal BD = 8.2 cm and angle between the diagonals = ${60}^{\circ }$
Step 1: Draw AC = 6.4 cm. Locate its midpoint as O
Identify the next step

1. Draw a line BOD such that ∠DOC = ${60}^{\circ }$ and OD = OB =½ BD = 4.1cm.
2. Draw a line COD such that ∠DOB =${60}^{\circ }$ and OD = OB =½ BD = 4.1cm.
3. Draw a line BOD such that ∠DOC = ${60}^{\circ }$ and OD = 3.5 cm and OB= 4.7cm.
   
4. None of these

Q. Lal is constructing a rectangle PQRS. The length of the diagonal is $6cm$ and the length of the sides are $3cm$ and $4cm$. Is the construction of the rectangle PQRS possible?

1. Yes
2. No
3. Yes, if the diagonal measures 5 cm.
4. Even, the changes in the length of the diagonal is not sufficient.

Q. Question 190
Construct a square of side 4 cm.

Q. To construct a square of diagonal AC =6.2 cm which of the following properties of a square do we use?

1. Diagonals bisect each other at ${90}^{\circ }$.
2. Diagonals are equal.
3. Both (A) and (C)
4. All sides are equal.

Q. The number of parameters required to construct a square is

1. One
2. Two
3. Three
4. Four

Q. Which properties of a square are different from properties of a parallelogram?

1. Diagonals are equal in length.
2. Diagonals bisect each other at ${90}^o.$
3. The opposite sides are equal in length.
4. The opposite sides are parallel.

Q. The number of variables required for the construction of a rectangle is ___.

Q. The number of variables required to construct a square is .

1. one
2. five
3. three
4. two

Q. A square cannot be constructed given only a diagonal of length 3 cm.

1. True
2. False

Q. To construct a square of diagonal AC =6.2 cm which of the following properties of a square do we use?

1. All sides are equal.
2. Both (A) and (C)
3. Diagonals are equal.
4. Diagonals bisect each other at ${90}^{\circ }$.

Q.

A rectangle WXYZ can be constructed if the length of

1. WX and ZY are given

2. XY is given

3. YZ is given

4. WX and WZ are given

Q. Arun is constructing a rectangle REMO where RE = 4 cm and RM = 5 cm. The steps for the construction is as follows:

(1) Draw a line segment RE of length 4 cm.
(2) Construct 90° at the points R and E. Extend the lines.
(3) Keeping R as the centre and a radius of 5cm, construct an arc cutting on the line generated from the point E.
(4) Mark the intersecting point to be M.
What is the next step?

1. Measure the length of the side EM for the construction of the side RO.
2. Join O and M. The rectangle REMO is hence constructed.
3. None of the above.
4. Keeping R as the centre, cut an arc of radius 3 cm on the generated from the point R.

Q. All squares are ______ but all _______ are not squares.
Which of the followings can fill the blank.

1. Rectangle
2. Parallelogram
3. Trapezoid
4. Rhombus

Q.

To construct a square only one length needs to be given.

1. True

2. False

Q. Lal is constructing a rectangle PQRS. The length of the diagonal is $6cm$ and the length of the sides are $3cm$ and $4cm$. Is the construction of the rectangle PQRS possible?

1. Yes, if the diagonal measures 5 cm.
2. Even, the changes in the length of the diagonal is not sufficient.
3. No
4. Yes

Q.

Suppose you are asked to construct a square having side length 'a' units. This information is enough to construct a square.

1. Draw line segment

2. Draw arc

Q. 69. Draw a square whose sides are represented by x=4, x=-4, y=4, y=-4 and find its area

Q. Question 198
Construct a square in which each diagonal is 5 cm long.

Q.

A rectangle WXYZ can be constructed if the length of

1. XY is given

2. YZ is given

3. WX and WZ are given

4. WX and ZY are given

Q. Draw a square WXYZ with side 5.2 cm.

Q.

Is it possible to construct a square if only one of its diagonals is given?

1. Yes

2. No

3. With 4 other measurements, Yes

4. With measurement of a side, Yes

Q. If we know that one side of a square is 6 cm, then we also know the length its diagonals and length of each side of the square.

1. True
2. False