Question

Rhombus is a parallelogram whose
a) diagonal bisect each other, not at right angle
b) diagonal bisect each other at right angle
c) diagonal does not bisect
d) none of the above

Answer 1

Answer:

RHOMBUSES

The Greeks took the word rhombos from the shape of a piece of wood that was whirled about the head like a bullroarer in religious ceremonies. This derivation does not imply a definition, unlike the words ‘parallelogram’ and ‘rectangle’, but we shall take their classical definition of the rhombus as our definition because it is the one most usually adopted by modern authors.

Definition of a rhombus

A rhombus is a quadrilateral with all sides equal.

First property of a rhombus − A rhombus is a parallelogram

Since its opposite sides are equal, a rhombus is a parallelogram − this was our second test for a parallelogram in the previous module. A rhombus thus has all the properties of a parallelogram:

Its opposite sides are parallel.

Its opposite angles are equal.

Its diagonals bisect each other.

It has rotation symmetry of order two about the intersection of its diagonals.

When drawing a rhombus, there are two helpful orientations that we can use, as illustrated below.

The rhombus on the left looks like a ‘pushed-over square’, and has the orientation we usually use for a parallelogram. The rhombus on the right has been rotated so that it looks like the diamond in a pack of cards. It is often useful to think of this as the standard shape of a rhombus.

Constructing a rhombus using the definition

It is very straightforward to construct a rhombus using the definition of a rhombus. Suppose that we want to construct a rhombus with side lengths 5cm and acute vertex angle 50°.

Draw a circle with radius 5cm.

Draw two radii OA and OB meeting at 50°

at the centre O.

Draw arcs with the same radius 5cm and centres

A and B, and let P be their point of intersection.

The figure OAPB is a rhombus because all its sides are 5cm

Step-by-step explanation:

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