Rhombi
1. Four congruent sides2. Diagonals are perpendicular 3. Diagonals bisect opposite angles
Rhombi (or rhombuses) are quadrilaterals with four sides of equal length. A rhombus has two pairs of parallel sides, where each pair is congruent but the opposite sides are not congruent. The opposite angles in a rhombus are equal, and the diagonals bisect each other at right angles.
To find the area of a rhombus, we can multiply the length of one diagonal by the length of the other diagonal and divide by two. Therefore, the area of a rhombus can be expressed as:
Area = (diagonal 1 × diagonal 2) / 2
To find the perimeter of a rhombus, we can simply add up the lengths of all four sides. Since all four sides are equal, we can also multiply the length of one side by four to obtain the perimeter.
One property of a rhombus is that it can be viewed as a special case of a parallelogram, where the two pairs of opposite sides are congruent. As a result, a rhombus has all the properties of a parallelogram, including opposite sides being parallel, opposite angles being congruent, and the consecutive angles being supplementary. However, unlike a general parallelogram, the diagonals of a rhombus are perpendicular to each other.
Finally, it is worth noting that a square is a special case of a rhombus, where all four sides are equal and all angles are right angles. Therefore, all properties and formulas that apply to a rhombus also apply to a square.
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