Definition: A rhombus is a quadrilateral with four congruent sides.
Similar to the definition of a rectangle, we could have used the word "parallelogram" instead of "quadrilateral" in our definition of rhombus. Thus, rhombuses have all of the properties of parallelograms (stated above), along with a few others.
Let's look at these properties.
(1) Consecutive sides of a rhombus are congruent.
(2) The diagonals of a rhombus bisect pairs of opposite angles.
(3) The diagonals of a rhombus are perpendicular.
If ABCD is a rhombus, then it has the following properties:
(i) Opposite sides are equal i.e. AB = DC and BC = AD
(ii) Opposite angles are equal i.e.
ÐA = ÐC and ÐB = ÐD
(iii) Diagonals bisect each other i.e.
AO = OC and BO = OD
Now, AB and AD are two adjacent sides of rhombus ABCD and adjacent sides of a rhombus are equal.
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