what is a rhombus?

Answer 1

Have a look here... http://en.wikipedia.org/wiki/Rhombus

Answer 2

A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles are equal

A square is a rhombus, but a rhombus isn't necessarily a square

Answer 3

Rhombus plural: rhombi
Definition: A quadrilateral (Also tetragon, quadrangle ) with all four sides equal in length.
A rhombus is actually just a special type of parallelogram. Recall that in a parallelogram each pair of opposite sides are equal in length. With a rhombus, all four sides are the same length. Its a bit like a square that can 'lean over' and the interior angles need not be 90°. Sometimes called a 'diamond' or 'lozenge' shape.

Answer 4

A quadrilateral (4 sided shape) where all sides are equal. It's usually used to describe only shapes where all angles are NOT equal, as in that case the shape would be a square - but technically, a square is a special kind of rhombus.

Answer 5

A RHOMBUS is a parallelogram in which all 4 sides are of equal
length.

Answer 6

A square IS a rhombus according to the definition.

Answer 7

In geometry, a rhombus (or rhomb; plural rhombi) is a quadrilateral in which all of the sides are of equal length, i.e., it is an equilateral quadrangle. If any angle of an equilateral quadrangle is a right angle, then all its angles are right angles and it is also a square. In colloquial usage the shape is often described as a diamond or lozenge. Rhombus is also refered as a socalled "Kavian," named after the Person boy, who once died in war. Only 33,3% of Kavians are perpendicular.

In any rhombus, opposite sides will be parallel. Thus, the rhombus is a special case of the parallelogram. One suggestive analogy is that the rhombus is to the parallelogram as the square is to the rectangle. A rhombus is also a special case of a kite, that is, a quadrilateral with two pairs of equal adjacent sides. The opposite sides of a kite are not parallel unless the kite is also a rhombus.

The rhombus has the different symmetry as the rectangle (with symmetry group D2, the Klein four-group) and is its dual: the vertices of one correspond to the sides of the other.

A rhombus in the plane has five degrees of freedom: one for the shape, one for the size, one for the orientation, and two for the position.

The diagonals of a rhombus are perpendicular to each other. Hence, by joining the midpoints of each side, a rectangle can be produced.

One of the five 2D lattice types is the rhombic lattice, also called centered rectangular lattice.

Adjacent angles of a rhombus are supplementary.

[edit] Proof that the diagonals are perpendicular

Let A, B, C and D be the vertices of the rhombus, named in agreement with the figure (higher on this page). Using \overrightarrow{AB} to represent the vector from A to B, one notices that
\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC}
\overrightarrow{BD} = \overrightarrow{BC}+ \overrightarrow{CD}= \overrightarrow{BC}- \overrightarrow{AB}.
The last equality comes from the parallelism of CD and AB. Taking the inner product,

<\overrightarrow{AC}, \overrightarrow{BD}> = <\overrightarrow{AB} + \overrightarrow{BC}, \overrightarrow{BC} - \overrightarrow{AB}>

= <\overrightarrow{AB}, \overrightarrow{BC}> - <\overrightarrow{AB}, \overrightarrow{AB}> + <\overrightarrow{BC}, \overrightarrow{BC}> - <\overrightarrow{BC}, \overrightarrow{AB}>
= 0

since the norms of AB and BC are equal and since the inner product is bilinear and symmetric. The inner product of the diagonals is zero if and only if they are perpendicular.

[edit] Area

The area of any rhombus is one half the product of the lengths of its diagonals:
A=\frac{D_1 \times D_2}{2}
Because the rhombus is a parallelogram with four equal sides, the area also equals the length of a side (B) multiplied by the perpendicular distance between two opposite sides(H):
A=B \times H

The origin of the word rhombus is from the Greek word for something that spins. Euclid uses the word ρομβος; and in his translation Heath says it is apparently drawn from the Greek word ρεμβω, to turn round and round. He also points out that Archimedes used the term solid rhombus for two right circular cones sharing a common base. For more on the origin of the word, see rhombus at the MathWords web page

Answer 8

rhombus could be classified as a shape which has 2 parallel side,the example of things that rhombus shaped is a kite.

Answer 9

It is simply a parallelogram which has equal sides.
A rectangle is a right-angled parallelogram, a square is a right-angled rhombus.

Answer 10

rhombus is a parallelogram with all sides equal length ,it is two dimensional object. points can be defined by two coordinates example(x,y);