Quadrilateral-Rhombus

A “Quadrilateral- rhombus” is a two-dimensional flat shape. It is an exceptional parallelogram and on account of the unique backdrops, it obtains a title as a “quadrilateral”. The rhombus is also known as “equilateral quadrilateral” because its edges are the same in length. The phrase “rhombus” has been collected from the age-old Greek word “rhombus”, which means top that spins. All the rhombuses are considered parallelograms, but the entire “parallelograms” are not “rhombuses”. The rhombus is not “squares”, but the entire “squares” are rhombuses. A “rhombus” consists of three different names: Rhomb, Diamond, and Lozenge.

Properties of rhombus

There are multiple properties of Rhombus that are listed below:

• All the edges of a “rhombus” are the same.
• The edges of a “rhombus” are parallel.
• The angles of the “rhombus” are the same.
• In a  “rhombus”, the diagonals intersect one another at the right angles.
• The total sum of dual “adjacent angles” is the same as “180 degrees”.
• The two different diagonals of the rhombus form four “right-angled” triangles that are concurrent to one another.
• By joining the midpoints of the edges, it will result in the formation of a rectangle.
• By joining the midpoints of the respective half of the diagonal, a “rhombus” will be formed.
• Around a “rhombus” there are no “circumscribing circles”.
• Within a “rhombus”, there are no engraving circles.
• When the “shorter diagonal” is the same as a single side of an individual rhombus, the two concurrent “equilateral triangles” are formed.
• The “diagonals” are at right angles and bisect one another.
• The “adjacent angles” are considered supplementary. The formula of “quadrilateral-rhombus” is:

“∠A + ∠B = 180°”

• A “rhombus” is a “parallelogram” whose horizontal lines are at right angles to one another.

Properties of   the Diagonals of a rhombus

The Diagonal of an individual rhombus consists of several properties that are listed below:

• They intersect one another at the right angles or 90 degrees.
• The two horizontal lines form the 4 concurrent “right-angled” triangles.
• The space of the mark of bisection two horizontal lines to the centre point of the edges will be considered as the radius of the “circumscribing” of one of the “4 right-angled” triangles.
• The region of a rhombus is considered as a “product” of the multiple lengths of the respective two diagonals.
• The horizontal lines intersect the angle inside of which they are interlinked.
•  The lines that are joining the centre points of the respective four edges in place, will form an individual rectangle whose width and length will be considered as half of that of chief horizontal lines.
• The area of a “rectangle” will be a quarter of that respective rhombus.
• If via the exact “point of intersection” of the respective two horizontal lines that draw lines similar to the edges, it will result in the formation of four concurrent rhombuses.   

Symmetry of rhombus

There are two “lines of symmetry” in a particular rhombus. The fictional line or the axis with which the “rhombus” can be crumpled for obtaining the two “symmetrical halves” is known as the “line of symmetry” in the rhombus. If the crumpled part precisely overlaid on the “other half”, along with the sides and corners accompanying, then the crumpled line illustrates a “line of symmetry” and that figure is symmetrical along the width, lengths, and its respective diagonals. The horizontal lines are two “lines of symmetry” inside a “rhombus”. This is due to the crumbling of the rhombus with the horizontal line, resulting in getting the equal figure as two different halves.

Proving a single quadrilateral is a “rhombus”:

• A “rhombus” is an individual parallelogram along with the same side lengths.
• A “rhombus” horizontally intersects the angles of vertices each horizontal line bisects.
• A “rhombus” has horizontal lines that are “perpendicular” to each other and intersect each other.

“Extension- Quadrilaterals whose diagonals are perpendicular”:

The discourse of a single property is irrelevant to a particular test. However, a specific “quadrilateral” with perpendicular horizontal lines is not considered as a “rhombus”. It can be done by placing two different sticks over one another at “right angles” and by joining the respective endpoints. The above-mentioned part of the proof is the application of the “Pythagoras’ theorem”. “One half” is straightforward and the other one wants proof by verification and an inventive construction.

Conclusion

The “quadrilateral-rhombus” is one of the main chapters of trigonometry. If one has to understand the concept of “quadrilateral-rhombus”, the individual must go through the chapter of Rhombus. To summarize the figure of a “rhombus” is symmetric through its horizontal lines, which mean there is the same portion along the two sides of the respective horizontal lines. That is, on the condition that a “rhombus” is divided through any of the horizontal lines, this will result in getting multiple “symmetrical shapes” of the same perimeter and area. The symmetric characteristics of a “rhombus” come mostly from the reality that the horizontal lines are the same and they intersect each other.