Properties of Squares

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.

1. Draw line segment

2. Draw arc

Q.

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

1. $8cm$

2. $4\sqrt{2}cm$

3. $8\sqrt{2}cm$

4. $4cm$

Q.

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

1. 1

2. 3

3. 2

4. 4

Q.

The diagonal of square are perpendicular to one another.

1. True
2. 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?

1. Equilateral
2. acute-angled triangle
3. Scalene
4. 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 $\angle AOB$?

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${30}^{\circ }$

4. ${45}^{\circ }$

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.

1. $\angle$ HDI = 30${}^{\circ }$

2. DI = JC = 3m

3. DI = JC = 4m

4. $\angle$ HDI = 45${}^{\circ }$

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 $\perp$ AC [4 MARKS]

Q.

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

1. Draw line segment

2. Draw arc

Q.

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

1. ${50}^{\circ }$

2. ${40}^{\circ }$

3. ${130}^{\circ }$

4. ${35}^{\circ }$

Q.

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

1. $4cm$

2. $3cm$

3. $6cm$

4. $12cm$

Q. Which figure must continue series of figure?

1. 3
2. 1
3. 4
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?

1. ${30}^{\circ }$

2. ${90}^{\circ }$

3. ${45}^{\circ }$

4. ${60}^{\circ }$

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 $\sqrt{2}$ times the diagonal of a square

1. True
2. False

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

1. one side
2. one diagonal
3. one angle
4. two angles

Q. Construct a quadrilateral $MORE$ where $MO=6cm$, $OR=4.5cm$ , $\angle M={60}^o$ , $\angle O={105}^o$ and $\angle R={105}^o$

Q. Counstruct a quadrilateral TRUE in which
TR=$3.5cm$
RU=$3cm$
UE=$4cm$
$\angle R={75}^{\circ }$
$\angle U={120}^{\circ }$

Q.

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

1. Diagonals are equal

2. Diagonals bisect each other at ${90}^{\circ }$.

3. Both (A) and (B)

4. All sides are equal

Q. Construct a cyclic quadrilateral ABCD when AB$=6$cm, BC$=5.5$cm, $\angle$ABC$={80}^o$ and AD$=4.5$cm.

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

1. $30$
2. $40$
3. $50$
4. $60$

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

Q. Construct a quadrilateral $ABCD$, when :
Angle $A={90}^{o}AB=4.6$ 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, $BC=3.8$cm, $CD=4.9$cm, $AD=5.4cm$ and $\angle B=72$. 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 $\angle ABX={72}^{\circ }$.
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 $CD$

1. $3$
2. $4$
3. $2$
4. $1$

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 $\angle A={45}^{\circ }$

Q.

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