# Properties of Squares

## Trending Questions

**Q.**

A picture frame is $80$ cm by$60$cm.Find its diagonal

**Q.**

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

Draw line segment

Draw arc

**Q.**

If a square has a side of length 4 cm, what is the length of the diagonal?

8 cm

4√2 cm

8√2 cm

4 cm

**Q.**

What are the minimum number of parameters required to construct a square?

1

3

2

4

**Q.**

The diagonal of square are perpendicular to one another.

- True
- False

**Q.**

Sita got a wooden square plate and cut it diagonally, as shown in the figure below. After cutting it, she saw that two triangles are formed.

Can you tell what type of triangles are formed?

- Equilateral
- acute-angled triangle
- Scalene
- Isosceles right-angled triangle

**Q.**

Question 110

Solve the following question:

Find the length of the side of a square, if the length of its diagonal is 10 cm.

**Q.**

In the square ABCD below, what is the measure of ∠AOB?

60∘

90∘

30∘

45∘

**Q.**

In the given figure, ABCD and EFGH are two squares of sides 4 cm and 10 cm respectively.

What additional information do you require to construct this combination of quadrilaterals?

Select all that apply.

∠ HDI = 30∘

DI = JC = 3m

DI = JC = 4m

∠ HDI = 45∘

**Q.**Why is 2 subtracted from the formula. -- (n-2)180

**Q.**ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB an parallel to BC intersects AC at D. Show that

MD ⊥ AC [4 MARKS]

**Q.**

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

Draw line segment

Draw arc

**Q.**

In the given figure, ABCD is a square. Then the value of 'x' is

50∘

40∘

130∘

35∘

**Q.**

In a square ABCD, if BD=6 cm, what is the length of AC ?

4 cm

3 cm

6 cm

12 cm

**Q.**Which figure must continue series of figure?

- 3
- 1
- 4
- 2

**Q.**

Consider two right-angled triangles inscribed in a square such that their hypotenuse intersect at a point O inside the square. What is the angle between the hypotenuse of the triangle and the base of the square?

30∘

90∘

45∘

60∘

**Q.**Construct the following quadrilaterals. Quadrilateral ABCD.

AB=4.5cm

BC=5.5cm

CD=4cm

AD=6cm

AC=7cm

**Q.**State the following statement is True or False

The side of a square is √2 times the diagonal of a square

- True
- False

**Q.**We can construct a square if any one of the following measurements is given. Choose the correct options.

- one side
- one diagonal
- one angle
- two angles

**Q.**Construct a quadrilateral MORE where MO=6 cm, OR=4.5 cm , ∠M=60o , ∠O=105o and ∠R=105o

**Q.**Counstruct a quadrilateral TRUE in which

TR=3.5cm

RU=3cm

UE=4cm

∠R=75∘

∠U=120∘

**Q.**

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

Diagonals are equal

Diagonals bisect each other at 90∘.

Both (A) and (B)

All sides are equal

**Q.**Construct a cyclic quadrilateral ABCD when AB=6cm, BC=5.5cm, ∠ABC=80o and AD=4.5cm.

**Q.**In the above figure, find the value of x, if the figure is a square.

- 30
- 40
- 50
- 60

**Q.**Construct a quadrilateral ABCD, when AB=3.5 cm, BC=4.8 cm, CD=5.1 cm, AD=4.4 cm and diagonal AC=5.9 cm.

**Q.**Construct a quadrilateral ABCD, when :

Angle A=90o AB=4.6 cm, BD=6.4 cm, AC=6 cm and CD=4.2 cm.

**Q.**For construction of a quadrilateral ABCD, where AB=4.2 cm, BC=3.8cm, CD=4.9cm, AD=5.4cm and ∠B=72. Its steps for construction is given in jumbled form. Identify the first step from the following:

1) From B, set off BC=3.8 cm.

2) Draw AB=4.2 cm and Make ∠ABX=72∘.

3) With A as center and radius equal to 5.4 cm draw an arc.

4) With C as center and radius equal to 4.9 cm, draw another arc, cutting the previous arc at D. Join AD and CD

- 3
- 4
- 2
- 1

**Q.**Construct a quadrilateral PQRS in which PQ=4.4cm, QR=4.0cm, RS=6.4cm, SP=2.8cm and QS=6.6cm. Measure the diagonal PR.

**Q.**

Construct the quadrilaterals with the given measurements and write steps of construction.

quadrilateral ABCD with AB=5.5cm, BC=3.5cm, CD=4cm, AD=5cm and ∠A=45∘

**Q.**

Measure of the angles of set-square with all unequal sides is _____, _______ and ______.