Construction of Rectangle When Ratio of Sides Are Given

Q.

The diagonals of a quadrilateral are perpendicular to each other. The midpoints of its sides are joined to form another quadrilateral. Then, this quadrilateral is a square.

1. False

2. True

Q.

The quadrilateral formed by joining the midpoints of a rhombus is a

1. Rectangle

2. Parallelogram

3. Square

4. Trapezium

Q. In the given figure, find the value $x$.

1. ${108}^o$
2. ${58}^o$
3. ${80}^o$
4. ${100}^o$

Q. When is the quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, a rhombus?

1. PQRS is a rhombus.
2. Diagonals of PQRS are perpendicular.
3. Diagonals of PQRS are equal.
4. PQRS is a parallelogram.

Q.

The quadrilateral formed by joining the midpoints of adjacent sides of the quadrilateral is a _______

1. Rectangle

2. Rhombus

3. Square

4. Parallelogram

Q.

The quadrilateral formed by joining the midpoints of adjacent sides of a rectangle is a _________

1. Square

2. Trapezium

3. Parallelogram

4. Rhombus

Q.

In triangle ABC , if X is the midpoint of AB and Y is the midpoint of AC, then XYCB is a _________

1. Parallelogram

2. Trapezium

3. Rectangle

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

Q.

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

1. Yes

2. Yes, if the measurement of one angle is given.

3. Yes, if the measurement of two angles are given.

4. No, its not possible