Let us keep aside rhombus for a moment and try to get a clear picture about a quadrilateral. What is a quadrilateral? A quadrilateral is a shape that is a polygon that is enclosed by four sides. 4 vertices and 4 angles enclosed with 4 sides. The sum of angles of a quadrilateral = 4 right angles = 360 degrees by angle sum property of quadrilateral. For a quadrilateral, in general, the sides and the angles of a quadrilateral will never be of the same length or measure.
Now that we have an idea about the properties of a quadrilateral, let us talk about some special types of quadrilaterals. Geometrical shapes like square, rectangle, trapezium, parallelogram, rhombus are special types of quadrilaterals. For a quadrilateral, in general, the sides and the angles will never be of the same length or measure. But a square is a special type of quadrilateral which has four equal sides and each angle is 90 degrees. Similarly, a rhombus is a quadrilateral in which all the sides are equal. Exact opposite sides are parallel and the exact opposite vertex angles are equal. Therefore, in this article, we shall learn how to construct a rhombus where the measurement of its two diagonals is given.
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.
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.
1) What are the 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.
2) How to Construct a Rhombus?
How to make a rhombus might be a question that would be bothering you here. Follow the steps given to learn how to draw a rhombus, with the help of a compass.
Step 1: Draw a vertical line segment LN of length 4 cm.
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.
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
Step 4: Now join the points L with M, M with N, N with O, and O with L.
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 ≤ NPO ≤ OPL = 90 degrees.
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