# 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 $90^o$ 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:
$\frac{product~of~the~diagonals}{2}=area~of~rhombus$

### 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?

Yes.

### Exercise #2

Given the rhombus:

Is every rhombus a square?

Not true

### Exercise #3

Given the rhombus:

Is every square a rhombus?

True

### Exercise #4

Given the rhombus:

How much is it worth? $∢D$?

30

### Exercise #5

Given the rhombus:

How much is it worth? $∢A$?

50

### Exercise #1

Given the rhombus:

How much is it worth? $∢B$?

130

### Exercise #2

Given the rhombus:

How much is it worth? $∢A$?

50

### Exercise #3

Given the rhombus:

How much is it worth? $∢B$?

140

### Exercise #4

Given the rhombus:

How much is it worth? $∢D$?

60

### Exercise #5

Given the rhombus:

How much is it worth? $∢C$?

150

### Exercise #1

Given the rhombus:

How much is it worth? $∢A$?

70

### Exercise #2

Given the rhombus:

How much is it worth? $∢B$?

130

### Exercise #3

Given the rhombus:

How much is it worth? $∢C$?

160

### Exercise #4

Given the rhombus:

Are the triangles formed by the diagonal congruent?

True

### Exercise #5

Given the rhombus:

Are the triangles formed by the diagonal congruent?

True