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# Construction of a Rhombus

A rhombus is a four-sided quadrilateral whose two pairs of opposite sides are equal. It is similar to a parallelogram. The diagonals of a rhombus have two lines of symmetry. It can be mirrored through its major diagonal. The general properties of a rhombus are:

1. The opposite sides of a rhombus are equal and congruent.
2. The opposing sides are parallel and equal.
3. The opposite sides of a rhombus are equal and congruent.
4. The sum of two adjacent or consecutive angles is equal to 180 degrees.

## Construction of a rhombus when the length of two diagonals are given

In a rhombus, the sides are of equal length. The opposite sides are parallel and equal. Let us consider that we need to construct a rhombus ABCD whose diagonals AC and BD are 6 and 7 cm, respectively. Therefore, we do not need any other dimension to construct a rhombus.

1. Draw the first diagonal of length 6 cm with the help of a ruler. Name the endpoints of these diagonals as A and C.
2. Now, we will need a compass. Take any radius on the compass of any length. With A as a centre, draw an arc both left and right of the line.
3. Repeat the same steps with C as the centre as well.
4. We will see the arcs cut each other at a specific point.
5. Join these points and name them B and D, respectively.
6. After measuring the other diagonal, we will get to know that the diagonal is 7 cm. If the diagonal is not 7 cm, there is an error while constructing the diagonal.
8. Therefore, ABCD is the required rhombus with diagonals 6 cm and 7 cm.

## Construction of a rhombus when one side and one angle are given

After knowing the construction of a rhombus when diagonals are given, we can construct a rhombus when one of its sides and its angles are given.

1. Firstly, we will construct the line segment whose length is given to us. Name this line segment as AB.
2. With the help of a protractor, we will construct the angle given to us with one end of the line segment. We need to make sure the angle we create must be an inner angle and not the outer angle. It means the angle must be formed inside the rhombus and not outside.
3. Take the compass and measure the length of the side on it.
4. With A as a centre, draw an arc in the direction where the angle was made.
5. Join the angle point and the arc. Name this point as C.
6. Now with C as a centre, draw an arc of the same length as given to us.
7. Repeat the steps till we get an enclosed figure. Name the final points like C and D.
8. Therefore, ABCD is the required rhombus.

## Construction of a rhombus when one side and one diagonal are given

We need to construct a rhombus whose one side and one diagonal is given to us.

1. Draw a line segment AB of the length given to us.
2. With A as a centre, construct an arc with a length equal to the diagonal of the rhombus.
3. Repeat the same step with B as centre as well. Name these points are C and D.
4. Join AD, CD and CB.
5. Therefore, the rhombus ABCD is the required rhombus.

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