properties of Rhombus
Answers
All the sides are equal.
Opposite angles of a rhombus are equal.
the diagonals of a rhombus bisect the interior angles.
the diagonal of a rhombus bisect each other at right angles.
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A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond. The plural form of a rhombus is rhombi or rhombuses.
Area of Rhombus, A = (d1 x d2)/2 square units
The perimeter of Rhombus, P = 4a units
Properties Of Rhombus
Some of the important properties of the rhombus are as follows:
•All sides of the rhombus are equal.
•The opposite sides of a rhombus are parallel.
•Opposite angles of a rhombus are equal.
•In a rhombus, diagonals bisect each other at right angles.
•Diagonals bisect the angles of a rhombus.
•The sum of two adjacent angles is equal to 180 degrees.
•The two diagonals of a rhombus form four right-angled triangles which are congruent to each other
•You will get a rectangle when you join the midpoint of the sides.
•You will get another rhombus when you join the midpoints of half the diagonal.
•Around a rhombus, there can be no circumscribing circle.
•Within a rhombus, there can be no inscribing circle.
•You will get a rectangle, where the midpoints of the 4 sides are joined together, and the length and width of the rectangle will be half the value of the main diagonal so that the area of the rectangle will be half of the rhombus.
•When the shorter diagonal is equal to one of the sides of a rhombus, two congruent equilateral triangles are formed.
•You will get a cylindrical surface having a convex cone at one end and concave cone at another end when the rhombus is revolved about any side as the axis of rotation.
•You will get a cylindrical surface having concave cones on both the ends when the rhombus is revolved about the line joining the midpoints of the opposite sides as the axis of rotation.
•You will get solid with two cones attached to their bases when the rhombus is revolving about the longer diagonal as the axis of rotation. In this case, the maximum diameter of the solid is equal to the shorter diagonal of the rhombus.
•You will get solid with two cones attached to their bases when the rhombus is revolving about the shorter diagonal as the axis of rotation. In this case, the maximum diameter of the solid is equal to the longer diagonal of the rhombus.