Construction of a Rectangle When One Diagonal and the Angle between the Two Diagonal Are Given.

Q.

Construct a rectangle ABCD ; if :

(i) AB = 4.5 cm and BC = 5.5 cm.

(ii) BC = 6.1 cm and CD = 6.8 cm.

(iii) AB = 5.0 cm and diagonal AC = 6.7 cm.

(iv) AD = 4.8 cm and diagonal AC = 6.4 cm.

(v) each diagonal is 6 cm and the angle between them is ${45}^{\circ }$.

(vi) each diagonal is 5.5 cm and the angle between them is ${60}^{\circ }$

Q.

To construct a rectangle ABCD given AC=6cm and angle between diagonals is ${30}^{\circ }$, which of the following properties of rectangles do we use?

1. Diagonals are equal.

2. Opposite sides are equal.

3. Diagonals bisect each other.

4. Diagonals are perpendicular to each other.

Q.

Which property of a rectangle do we use to construct a rectangle ABCD with each diagonal AC= 6.2cm.

1. Each angle of a rectangle is ${90}^{\circ }$.
2. Opposite sides are equal.
3. Diagonals bisect each other.
4. Both (A) and (B)

Q. Using ruler and compasses only, construct a rectangle each of whose diagonals measures 6 cm and the diagonals intersect at an angle of ${45}^{\circ }$.

Q. Construct a rectangle whose diagonal = 5.8 cm and angle between the diagonals is ${50}^{\circ }$.

Q. In the adjacent figure, we have $BX=\frac{1}{2}AB,BY=\frac{1}{2}BC$ and $AB=BC$. Show that $BX=BY$

Q. The length of the rectangle is _____ $cm$.

1. $8.1$
2. $9.2$
3. $6.4$
4. $5.6$

Q.
Construct a rectangle ABCD given AC=6cm and angle between diagonals is ${30}^{\circ }$.

$\left[3\right]$

Q. The breadth of the rectangle formed is of length ____ $cm$.

1. $3.4$
2. $4.2$
3. $2.2$
4. $1.6$

Q.

Which property of a rectangle do we use to construct a rectangle given one diagonal and angle between diagonals?

1. Opposite sides are equal

2. Diagonals are equal
   

3. Diagonals bisect each other
   

4. Both (A) and (B)
   

Q. One diagonal = $6.0$ cm and the angle between the diagonals = ${45}^{\circ }$.

Q.

To construct a rectangle ABCD given AC=6cm and angle between diagonals is ${30}^{\circ }$, which of the following properties of rectangles do we use?

1. Diagonals are equal.

2. Opposite sides are equal.

3. Diagonals bisect each other.

4. Diagonals are perpendicular to each other.