The diagonals of a rhombus have 3 properties that we can use without having to prove them:

The diagonals of a rhombus have 2 properties that we must prove to use them:

Other properties:

  • The lengths of the diagonals of a rhombus are not equal.

The product of the diagonals divided by 2 is equal to the area of the rhombus:
product of the diagonals2=area of rhombus\frac{product~of~the~diagonals}{2}=area~of~rhombus

Diagonals of a rhombus

A - Diagonals of a rhombus

Suggested Topics to Practice in Advance

  1. Rhombus, kite, or diamond?

Practice Diagonals of a Rhombus

Examples with solutions for Diagonals of a Rhombus

Exercise #1

Do the diagonals of the rhombus above intersect each other?

Step-by-Step Solution

In a rhombus, all sides are equal, and therefore it is a type of parallelogram. It follows that its diagonals indeed intersect each other (this is one of the properties of a parallelogram).

Therefore, the correct answer is answer A.

Answer

Yes

Exercise #2

Look at the following rhombus:

Are the diagonals of the rhombus parallel?

Step-by-Step Solution

The diagonals of the rhombus intersect at their point of intersection, and therefore are not parallel

Answer

No.

Exercise #3

Look at the following rhombus:

Are the diagonals of the rhombus perpendicular to each other?

Step-by-Step Solution

The diagonals of the rhombus are indeed perpendicular to each other (property of a rhombus)

Therefore, the correct answer is answer A.

Answer

Yes.

Exercise #4

Given the rhombus:

BBBAAACCCDDD50

How much is it worth? A ∢A ?

Video Solution

Step-by-Step Solution

The rhombus is a type of parallelogram, therefore its opposite angles are equal (property of parallelograms), so:

A=50° ∢A =50\degree Therefore, the correct answer is answer A.

Answer

50

Exercise #5

Look at the following rhombus:

Can a rhombus have diagonals that are equal?

Video Solution

Answer

Yes.

Exercise #6

Given the rhombus:

BBBAAACCCDDD30

How much is it worth? D ∢D ?

Video Solution

Answer

30

Exercise #7

Given the rhombus:

BBBAAACCCDDD130

How much is it worth? B ∢B ?

Video Solution

Answer

130

Exercise #8

Given the rhombus:

BBBAAACCCDDD50

How much is it worth? A ∢A ?

Video Solution

Answer

50

Exercise #9

Given the rhombus:

Is every rhombus a square?

Video Solution

Answer

Not true

Exercise #10

Given the rhombus:

Is every square a rhombus?

Video Solution

Answer

True

Exercise #11

Given the rhombus:

BBBAAACCCDDD20

How much is it worth? B ∢B ?

Video Solution

Answer

140

Exercise #12

Given the rhombus:

BBBAAACCCDDD60

How much is it worth? D ∢D ?

Video Solution

Answer

60

Exercise #13

Given the rhombus:

BBBAAACCCDDD15

How much is it worth? C ∢C ?

Video Solution

Answer

150

Exercise #14

Given the rhombus:

BBBAAACCCDDD55

How much is it worth? A ∢A ?

Video Solution

Answer

70

Exercise #15

Given the rhombus:

BBBAAACCCDDD25

How much is it worth? B ∢B ?

Video Solution

Answer

130

Topics learned in later sections

  1. The Area of a Rhombus
  2. From Parallelogram to Rhombus