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:
$\frac{product~of~the~diagonals}{2}=area~of~rhombus$

Diagonals of a rhombus

Detailed explanation

Practice Diagonals of a rhombus

Question 1

Look at the following rhombus:

Are the diagonals of the rhombus parallel?

Question 2

Look at the following rhombus:

Can a rhombus have diagonals that are equal?

Question 3

Given the rhombus:

Is every rhombus a square?

Question 4

Given the rhombus:

Is every square a rhombus?

Question 5

Given the rhombus:

How much is it worth? $$ ∢D $$ ?

examples with solutions for diagonals of a rhombus

Exercise #1

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 #2

Look at the following rhombus:

Can a rhombus have diagonals that are equal?

Video Solution

Answer

Yes.

Exercise #3

Given the rhombus:

Is every rhombus a square?

Video Solution

Answer

Not true

Exercise #4

Given the rhombus:

Is every square a rhombus?

Video Solution

Answer

True

Exercise #5

Given the rhombus:

How much is it worth? $∢D$ ?

Video Solution

Answer

Question 1

Given the rhombus:

How much is it worth? $$ ∢A $$ ?

Question 2

Given the rhombus:

How much is it worth? $$ ∢B $$ ?

Question 3

Given the rhombus:

How much is it worth? $$ ∢A $$ ?

Question 4

Given the rhombus:

How much is it worth? $$ ∢B $$ ?

Question 5

Given the rhombus:

How much is it worth? $$ ∢D $$ ?