Diagonals of a rhombus - Examples, Exercises and Solutions

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

  • The diagonals of a rhombus intersect. (not only do they intersect, but they do so exactly at the midpoint of each one).
  • The diagonals of a rhombus are perpendicular, forming a right angle of 90o 90^o degrees.
  • The diagonals of a rhombus cross the angles of the rhombus.

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

  • The diagonals of a rhombus form four congruent triangles.
  • The diagonals of a rhombus create equal alternate angles.

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

Exercise #1

Look at the following rhombus:

Can a rhombus have diagonals that are equal?

Video Solution

Answer

Yes.

Exercise #2

Given the rhombus:

Is every rhombus a square?

Video Solution

Answer

Not true

Exercise #3

Given the rhombus:

Is every square a rhombus?

Video Solution

Answer

True

Exercise #4

Given the rhombus:

BBBAAACCCDDD30

How much is it worth? D ∢D ?

Video Solution

Answer

30

Exercise #5

Given the rhombus:

BBBAAACCCDDD50

How much is it worth? A ∢A ?

Video Solution

Answer

50

Exercise #1

Given the rhombus:

BBBAAACCCDDD130

How much is it worth? B ∢B ?

Video Solution

Answer

130

Exercise #2

Given the rhombus:

BBBAAACCCDDD50

How much is it worth? A ∢A ?

Video Solution

Answer

50

Exercise #3

Given the rhombus:

BBBAAACCCDDD20

How much is it worth? B ∢B ?

Video Solution

Answer

140

Exercise #4

Given the rhombus:

BBBAAACCCDDD60

How much is it worth? D ∢D ?

Video Solution

Answer

60

Exercise #5

Given the rhombus:

BBBAAACCCDDD15

How much is it worth? C ∢C ?

Video Solution

Answer

150

Exercise #1

Given the rhombus:

BBBAAACCCDDD55

How much is it worth? A ∢A ?

Video Solution

Answer

70

Exercise #2

Given the rhombus:

BBBAAACCCDDD25

How much is it worth? B ∢B ?

Video Solution

Answer

130

Exercise #3

Given the rhombus:

BBBAAACCCDDD80

How much is it worth? C ∢C ?

Video Solution

Answer

160

Exercise #4

Given the rhombus:

BBBAAACCCDDD

Are the triangles formed by the diagonal congruent?

Video Solution

Answer

True

Exercise #5

Given the rhombus:

BBBAAACCCDDD

Are the triangles formed by the diagonal congruent?

Video Solution

Answer

True

Topics learned in later sections

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