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Rhombus

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Rhombus

Study Guide

Key Definition

A rhombus is a parallelogram with four congruent sides. The opposite angles of a rhombus are also congruent.

Important Notes

All sides of a rhombus are of equal length: $AB = BC = CD = DA$
Opposite angles are congruent: $\angle A = \angle C$ and $\angle B = \angle D$
The diagonals of a rhombus bisect each other at right angles
The area of a rhombus can be calculated as $Area = b \times h$
The area of a rhombus can also be calculated using diagonals: $Area = \frac{1}{2} d_1 d_2$
The perimeter of a rhombus is four times the length of one side ($Perimeter = 4a$, where a is the side length)

Mathematical Notation

$d_1, d_2$ represent the lengths of the diagonals

$h$ represents the height (distance between base and opposite side)

$a$ represents the length of one side

Use these notations when solving rhombus problems

Why It Works

The properties of a rhombus derive from its definition as an equilateral parallelogram, leading to interesting symmetry and congruence in its angles and diagonals.

Remember

A rhombus is a special parallelogram with equal sides and diagonals that bisect each other at right angles.

Quick Reference

Area Formula:$Area = b \times h$

Perimeter Formula:$Perimeter = 4a$ (where a is the side length)

Understanding Rhombus

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A rhombus is a four-sided shape with all sides of equal length. Its opposite angles are also equal.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the area of a rhombus with a base of $5 \text{ cm}$ and a height of $4 \text{ cm}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have a kite in the shape of a rhombus. Each side of the kite measures $6 \text{ m}$. Calculate the perimeter.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A rhombus has diagonals measuring $8 \text{ cm}$ and $6 \text{ cm}$. What is its area?

Challenge Quiz

Single Choice Quiz

Advanced

If a rhombus has an angle of $60^\circ$, what is the measure of its opposite angle?

Recap

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Review key concepts and takeaways