Quadrilaterals and Their Properties

Q.

All the sides of ----------------- and -------------------- are equal in length.

Q.

ABCD is a rhombus. If $\angle BCA={35}^{\circ }$ then

$\angle ADC=$ ___.

1. ${90}^{\circ }$

2. ${110}^{\circ }$

3. ${60}^{\circ }$

4. ${115}^{\circ }$

Q.

Which basic property of a square will you use, if you are asked to draw a square with diagonal measuring 5 cm?

1. All the sides of a square are equal.

2. All 4 angles of a square are right angles.

3. The angle between a side and a diagonal of a square is ${45}^{\circ }$

4. We cannot draw a square if only the length of diagonal is given.

Q.

If the diagonals of a rhombus are equal, then the rhombus is a_____

1. Rectangle

2. Parallelogram

3. Square

4. Kite

Q. The minimum number of measurements required to determine a quadrilateral is:

1. 3
2. 4
3. 5
4. 6

Q. The measurements of a quadrilateral are given as $AB=4cm,CD=5cm,\angle ABC={75}^{\circ },\angle BCD={45}^{\circ }$ and $\angle CDA={135}^{\circ }$.
Can you constant a unique quadrilateral ABCD?

1. $\text{Yes}$
2. $\text{No}$
3. $\text{With the measure of}\angle DAB,\text{yes}$.
4. $\text{With the measure of BC, yes}$.

Q.

If the diagonals of a quadrilateral bisect each other, then it could be

1. Rectangle

2. Parallelogram
   

3. Square
   

4. Kite

Q. The next figure in the following series will have ___ vertices.

1. 7
2. 8
3. 9
4. 10

Q. A quadrilateral PQRS is to be constructed. Lenghts of PQ, QR, PS, and PR are known. Which additional measurement is required to construct PQRS uniquely?

1. $\angle PSQ$
2. $QS$
3. $\angle QRP$
4. $\angle QPR$

Q.

The given figure is a rectangle in which $x:y=3:7$

Find angle $xandy.$

1. $x={27}^{\circ }$

   $y={63}^{\circ }$

2. $x={63}^{\circ }$

   $y={27}^{\circ }$

3. $x={21}^{\circ }$

   $y={69}^{\circ }$

4. $x={65}^{\circ }$

   $y={23}^{\circ }$

Q. At my farmhouse I am facing East, then I turn left and walk 10 metres. I again turn right and walk 5 metres. Again, I go 5 metres towards the South, and from there walk 5 metres towards the West. In which direction am I from my farmhouse?

1. East
2. West
3. North
4. South

Q. If length of the diagonals of rhombus ABCD are 8 cm and 6 cm, then each of its sides is .

1. 10 cm
2. 5 cm
3. 7 cm
4. 4 cm

Q. Which of the following is not a parallelogram?

1. Rhombus
2. Rectangle
3. Square
4. Trapezium

Q. equal is not the property of a rectangle.

1. Opposite sides
2. Diagonals
3. Adjacent sides

Q. Match the following with the values of 'x'.

1. 90°
2. 100°
3. 75°

Q.

The diagonals of a kite bisect each other.

1. False
2. True

Q. Given below is a parallelogram ABCD. Find the value of $x$ and $y$.

(3 marks)

Q. Construct a square of side 4 cm. (3 marks)

Q.

Which of the following is a parallelogram?

1. Rectangle

2. Square

3. Rhombus

4. All of these

Q. In the figure given below, all the four sides are equal. The construction of which figure is shown in the diagram?

1. Trapezium
2. Rhombus
3. Kite
4. Rectangle

Q. ___ is a quadrilateral whose diagonals are equal and bisect each other at right angles.

1. Square
2. Rhombus
3. Rectangle
4. Kite