Rectangle Construction Given 1 Side and 1 Diagonal

Q.

For which of the following figures, all angles are equal?

1. Rectangle

   

2. Kite

   

3. Trapezium

   

4. Rhombus

   

Q. Choose the correct order for the construction of the rectangle ABCD with AB = 6 cm and BC = 4 cm.

1. Construct a perpendicular AE to AB at A such that AE is greater than 4 cm.
2. With D as centre and radius 6 cm, draw an arc.
3. With A as centre and radius 4 cm draw an arc so as to cut AE at D.
4. Draw a line segment AB = 6cm.
5. With B as centre and radius 4 cm, draw another arc so as to intersect previous arc at C.
6. Join DC and BC. Then ABCD is the required rectangle

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

Q. Construct a rectangle ABCD, when:

Q.

Which of the following properties are used in the construction of a rectangle given the length of a side and a diagonal?

1. Every angle of a rectangle is a right angle

2. The diagonals bisect each other

3. The diagonals bisect each other at right angles

4. The diagonals of a rectangle do not bisect the angle at the vertex

Q. Sort the steps to construct a rectangle ABCD using the given measurements AB = 5 cm and BC = 12 cm.

1. Draw AB
2. $\left(CYperpendiculartoBC\right]$
3. Mark BC on $\overrightarrow{BX}$
4. $\left(DrawBXat90°\right]$
5. Connect AD

Q. Draw the following:
The square READ with $RE=5.1$ cm.

Q. Sort the steps to construct a rectangle ABCD using the given measurements AB = 5 cm and BC = 12 cm.

1. Draw AB
2. $\left(CYperpendiculartoBC\right]$
3. Mark BC on $\overrightarrow{BX}$
4. $\left(DrawBXat90°\right]$
5. Connect AD

Q. Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.

Q. Draw a line segment PQ of length 7 cm. Mark a point R on it, such that l(PR) : l(RQ) = 4 : 1.

Q.

Which of the following properties are used in the construction of a rectangle given the length of a side and a diagonal?

1. Every angle of a rectangle is a right angle

2. The diagonals bisect each other

3. The diagonals bisect each other at right angles

4. The diagonals of a rectangle do not bisect the angle at the vertex

Q. Find the spot of quadrilaterals in the given diagram according to their properties.

1. Kite
2. Rhombus
3. Trapezium

Q. Draw the following:
A rectangle with adjacent sides of lengths $5cm$ and $4cm$.

Q.

Which of the following properties are used in the construction of a rectangle given the length of a side and a diagonal?

1. Every angle of a rectangle is a right angle

2. The diagonals bisect each other

3. The diagonals bisect each other at right angles

4. The diagonals of a rectangle do not bisect the angle at the vertex

Q. Find the area of a trapezium-shaped field, the lengths of whose parallel sides are $42$ metre and $30$ metre and other sides are $18$ metre and $18$ metre.

Q. Using the measurements of 2 adjacent sides of a rectangle, we can construct it.

1. False
2. True

Q. What is the minimum number of measurements are required for the construction of a rectangle?

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

Q.

If we know that one side of the rectangle is 8 cm can we construct a unique rectangle?

1. Yes, we can

2. With measurement of two angles, yes

3. No, its not possible

4. With measurement of one angle, yes

Q.

What property of a rectangle do we use if we need to construct a rectangle whose adjacent sides are given?

1. Diagonals bisect each other.

2. Diagonals are equal.

3. Each angle of a rectangle is ${90}^{\circ }.$

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