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Exploring the geometry of a rhombus reveals its unique properties as a quadrilateral with equal-length sides and parallel opposite sides. This text delves into the parallelogram properties of rhombuses, their distinctive features such as perpendicular diagonals, and methods for calculating their area. Understanding these aspects is crucial for solving geometric problems involving this intriguing shape.

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## Definition of a Rhombus

### Special type of quadrilateral

A rhombus is a four-sided shape with equal sides and parallel opposite sides

### Member of the parallelogram family

Common features with other parallelograms

Rhombuses share properties such as parallel opposite sides, equal opposite angles, and bisecting diagonals with other parallelograms

### Uniquely defined by equilateral sides

The defining characteristic of a rhombus is its four equal sides

## Properties of a Rhombus

### Inherited properties of parallelograms

Rhombuses have parallel opposite sides, equal opposite angles, and bisecting diagonals like other parallelograms

### Diagonals intersect at right angles

The diagonals of a rhombus form perpendicular lines

### Diagonals bisect angles

The diagonals of a rhombus divide its angles into two equal parts

## Calculating the Area of a Rhombus

### Formula using diagonals

The area of a rhombus can be found by multiplying half the product of its diagonals

### Formula using base and height

The area of a rhombus can also be calculated by multiplying its base and height

### Always expressed in square units

The area of a rhombus is always measured in square units

## Solving Problems Involving Rhombuses

### Utilizing specific properties and definitions

To solve problems involving rhombuses, one must understand their unique properties and definitions

### Demonstrating perpendicular diagonals

Proving that the diagonals of a rhombus are perpendicular requires showing that they form right angles

### Understanding relationships between diagonals, angles, and sides

To find unknown measurements in a rhombus, one must understand the connections between its diagonals, angles, and sides

Algorino

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