Rhombus (from the ancient Greek ῥόΜβος and from the Latin rombus "tambourine") is a parallelogram, which is characterized by the presence of sides of the same length. In the case when the angles are 90 degrees (or a right angle), such a geometric figure is called a square. A rhombus is a geometric figure, a kind of quadrangles. Can be both a square and a parallelogram.
Origin of this term
Let's talk a little about the history of this figure, which will help to reveal a little the mysterious secrets of the ancient world. The familiar word for us, often found in school literature, “rhombus”, originates from the ancient Greek word “tambourine”. In ancient Greece, these musical instruments were made in the form of a rhombus or square (as opposed to modern fixtures). Surely you have noticed that the card suit - a tambourine - has a rhombic shape. The formation of this suit goes back to the times when round tambourines were not used in everyday life. Therefore, the rhombus is the oldest historical figure that was invented by mankind long before the advent of the wheel.
For the first time, such a word as "rhombus" was used by such famous personalities as Heron and the Pope of Alexandria.
Rhombus Properties
- Since the sides of the rhombus are opposite to each other and are pairwise parallel, the rhombus is undoubtedly a parallelogram (AB || CD, AD || BC).
- Rhombic diagonals intersect at right angles (AC ⊥ BD), and therefore are perpendicular. Therefore, the intersection bisects the diagonals.
- The bisectors of rhombic angles are the diagonals of the rhombus(∠DCA=∠BCA, ∠ABD=∠CBD, etc.).
- From the identity of parallelograms it follows that the sum of all the squares of the diagonals of a rhombus is the number of the square of the side, which is multiplied by 4.
Signs of a diamond
Rhombus in those cases is a parallelogram when it meets the following conditions:
- All sides of a parallelogram are equal.
- The diagonals of the rhombus intersect a right angle, that is, they are perpendicular to each other (AC⊥BD). This proves the rule of three sides (sides are equal and at 90 degrees).
- The diagonals of a parallelogram share the angles equally since the sides are equal.
Rhombus area
The area of a rhombus can be calculated using several formulas (depending on the material provided in the problem). Read on to find out what the area of a rhombus is.
- The area of a rhombus is equal to the number that is half the product of all its diagonals.
- Since a rhombus is a kind of parallelogram, the area of a rhombus (S) is the number of the product of the sideparallelogram to its height (h).
- Also, the area of a rhombus can be calculated using the formula that is the product of the squared side of the rhombus and the sine of the angle. The sine of the angle - alpha - the angle between the sides of the original rhombus.
- A formula that is the product of twice the angle alpha and the radius of the inscribed circle (r) is considered quite acceptable for the correct solution.
These formulas you can calculate and prove based on the Pythagorean theorem and the rule of three sides. Many of the examples are focused on using multiple formulas in one task.
