A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent.

There are several formulas for the rhombus that have to do with its

- Sides(click for more detail)
- all 4 sides are congruent

- Angles(click for more detail)
- diagonals bisect vertex angles

- Diagonals(click for more detail)
- diagonals are perpendicular

- Area (click for more detail)

A square is a rhombus and a rectangle. In other words, if each angle of a rhombus is 90°, then it's a square.

Probably the most famous rhombus out there is the baseball diamond. The distance between each base is the same, making the shape a rhombus!

### Rhombus Sides

All sides of a Rhombus are congruent.

AB BC CD AD### Rhombus **Practice** Problems

Since this shape is a rhombus you can set any of its sides equal to each other.

### Diagonals of a Rhombus

- AOD = 90°
- AOB = 90°
- BOC = 90°
- COD = 90°

The shape below is not a rhombus because its diagonals are not perpendicular.

However, since opposite sides are congruent and parallel, and the diagonals bisect each other. The shape below is a parallelogram.

### Angles of a Rhombus

The diagonals bisect the vertex angles of a rhombus. A proof of this property of the diagonals

##### Problem 5

##### Problem 6

Since the diagonals of a rhombus are perpendicular, these outside angles must be complementary angles.

##### Problem 7

Since diagonals bisect vertex angles, BCA ACD

##### Problem 8

### Area of Rhombus

**The formula for area of A Rhombus**

Area = ½(diagonal

_{1}× diagonal

_{2})

##### Problem 9

Area = ½(IK ×HJ) = ½ (9 ×12) = 54

### Putting It All Together

STAR is a rhombus. The measure of diagonals SA is 24 and the measure of TR is 10, what is the perimeter of this rhombus?

Ask yourself: What is true about the angles formed by the diagonals of a rhombus?

The angles, are perpendicular!

Now, what is true about the diagonals of all parallelograms?

The diagonals of parallelograms bisect each other.

Therefore, ZA = 12, ZT = 5

What kind of triangle is ZTA?

A Right Triangle!

So you can use the Pythagorean theorem to find the measure of side TA

Now, that you know the length of TA? How can you use the fact that the sides of a rhombus are congruent to finish this problem?

Since, all 4 sides must be 13.

The perimeter = 13 + 13 + 13 +13 = 52