[Maths Class Notes] on Construction of a Rhombus Pdf for Exam

Properties of a Rhombus

• By definition, all the sides of a rhombus are congruent. 

• The angles are bisected with the help of diagonals.

• The diagonals bisect each other perpendicularly. They are known as perpendicular bisectors. 

• All the properties of a parallelogram apply to the rhombus.

• The opposite angles in the rhombus are always congruent to each other.

• The consecutive angles in the rhombus are supplementary.

Rhombus Construction Steps

Let us say, we are asked to draw a rhombus LMNO with the length of its two diagonals. Let the diagonal LN = 4 cm and the diagonal OM = 5 cm. We must know the theorem that diagonals of a rhombus bisect each other at the right angle. Hence, we will not need any further dimensions to proceed with our construction of a rhombus.

Step 1:

Draw a vertical line segment LN of length 4 cm.

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Step 2: 

Place the compass at point L with any radius and from there draw an arc to the right and left respectively of the line segment LM. Similarly, repeat the process by placing the compass at point M. There should not be any change in the radius.

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Step 3:

Mark the centre as P. Draw the second diagonal OM = 5 cm, to connect the two arc points intersecting each other so that PO = PM = 7 / 2 = 3.5 cm

         

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Step 4:

Now join the points L with M, M with N, N with O, and O with L.

 

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Then, LMNO is the required rhombus with the diagonals measuring 4 cm and 5 cm respectively. Let us keep in mind that P is the center of the two diagonals and < LPM = < MPN [leq] NPO [leq] OPL = 90 degrees.