What are the basic properties of a rhombus?
A rhombus is a quadrilateral that has the following four properties:
- Opposite angles are equal.
- All sides are equal and, opposite sides are parallel to each other.
- Diagonals bisect each other perpendicularly.
- Sum of any two adjacent angles is 180°
Does a rhombus are congruent?
All sides of a rhombus are congruent, so opposite sides are congruent, which is one of the properties of a parallelogram. , all 4 sides are congruent (definition of a rhombus).
Do diagonals bisect each other in rhombus?
The opposite sides of a rhombus are parallel. The opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each vertex angle. The diagonals of a rhombus bisect each other at right angles.
How do you prove a rhombus is congruent?
If two consecutive sides of a parallelogram are congruent, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).
What are the fundamental properties of a rhombus?
Fundamental properties of the rhombus. 1 • All sides of the rhombus are equal. 2 • The opposite sides of a rhombus are parallel. 3 • The opposite angles of a rhombus are equal. 4 • In a rhombus, the diagonals bisect each other at right angles. 5 • The diagonals bisect the interior angles of the rhombus.
Are there any formulas for the side of rhombus?
Side of rhombus formulas: 1 Formula of rhombus side in terms of area and height: a = S ha 2 Formulas of rhombus side in terms of area and sine of any angle: a = √ S √ sinα a = √ S √ sinβ 3 Formula of rhombus side in terms of area and inradius: a = S 2 r 4 Formula of rhombus side in terms of it diagonals: a = √ d12 + d22 2
How many interior angles are there in a rhombus?
Rhombus has four interior angles. The sum of interior angles of a rhombus add up to 360 degrees. The opposite angles of a rhombus are equal to each other. The adjacent angles are supplementary. In a rhombus, diagonals bisect each other at right angles. The diagonals of a rhombus bisect these angles.
How to find the diagonal of a rhombus?
Diagonals of a rhombus formulas: 1. Formulas of rhombus longer diagonal in terms of side and cosine of any angle ( cosα or cosβ) d1 = a √ 2 + 2 * cosα d1 = a √ 2 – 2 * cosβ. 2. Formulas of rhombus smaller diagonal in terms of side and cosine of any angle ( cosα or cosβ) d2 = a √ 2 + 2 * cosβ d2 = a √ 2 – 2 * cosα. 3.
