Maths

Properties of Rhombus

What is a rhombus?

The rhombus is a quadrilateral because it has four sides (and four corners), and it is a parallelogram because it has opposite sides that are parallel (and congruent).

Rhombus Properties
Rhombus Properties

Rhombus Properties

  • The opposite sides are parallel.
  • The rhombus has a major diagonal and a minor diagonal perpendicular to each other; in fact, in the center, we find four right angles.
  • Diagonals bisect (i.e., divide in half) and are also corner bisectors.
  • The major diagonal divides the rhombus into two congruent isosceles triangles.
  • The smaller diagonal divides the rhombus into two isosceles triangles with congruent sides (if the smaller diagonal measures the side, it can also result in two congruent equilateral triangles).
  • The rhombus has 4 equal sides (in fact, the measure of only one is enough to calculate the perimeter), two acute angles equal to each other (at opposite vertices) and two obtuse angles equal to each other (at opposite vertices).
  • The rhombus has four sides in the same way as a measure. The sides are parallel two by two, that is, side AB is parallel to side CA. Side BC is parallel to side AD.
  • The rhombus is not a square because although the sides are the same, the internal angles are not right angles, that is, they are not 90°.

Parts of the rhombus.

Combining two opposite vertices we obtain the two diagonals, that is, the vertical diagonal that we can indicate with d 1, and the horizontal diagonal AC that we can indicate with d 2.

The two diagonals are not the same size, otherwise, it would be a square.

  • Opposite corners are equal, that is Angle ABC = Angle ADC, Angle BAC = Angle DCB.
  • The sum of the internal angles is 360°, i.e. (4 sides – 2) x 180° = 2 x 180° = 360°.
  • Each diagonal is also a bisector, that is, it divides the angles into two equal parts.
  • The two diagonals are orthogonal to each other, that is, they form an angle of 90 °, that is, a right angle.

Is Square a Rhombus?

A square, like a rhombus, has the same number of sides. In addition, the square’s diagonals are perpendicular to one another and cut through the opposing angles. A rhombus is thus a square.

Rhombus Angles

The following are some crucial rhombus angles facts:

  • The interior angles of a rhombus are four.
  • A rhombus’ internal angles add up to 360 degrees when added together.
  • In a rhombus, the opposite angles are equal.
  • Complementary angles are those that are next to each other.
  • Diagonals in a rhombus are at right angles to each other.
  • These angles are divided by the diagonals of a rhombus.

Rhombus Formulas

The rhombus formulas are defined by two major characteristics, such as:

  • Area
  • Perimeter

How to find Area of Rhombus?

The area of a rhombus is the area that it covers in a two-dimensional plane. The area is calculated by dividing the product of the rhombus’ diagonals by two. It’s written like this:

Area of Rhombus, X = (d1 x d2)/2 square units

How to find Perimeter of Rhombus?

The total length of a rhombus’s boundaries is its perimeter. The circumference of a rhombus is equal to the sum of its four sides. The formula for calculating its perimeter is:

The perimeter of Rhombus, P = 4x units

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