From a parallelogram to a rhombus - Examples, Exercises and Solutions

You will be able to determine that the parallelogram is a rhombus if at least one of the following conditions is met:

  1. If in the parallelogram there is a pair of adjacent equal sides - it is a rhombus.
  2. If in the parallelogram the diagonals bisect each other, forming angles of 90o 90^o degrees, that is, they are perpendicular - it is a rhombus.
  3. If in the parallelogram one of the diagonals is the bisector - it is a rhombus.

Suggested Topics to Practice in Advance

  1. Rhombus, kite, or diamond?
  2. Diagonals of a Rhombus
  3. The Area of a Rhombus

Practice From a parallelogram to a rhombus

Exercise #1

Given the parallelogram:

AAABBBDDDCCC7575

Is this parallelogram a rhombus?

Video Solution

Answer

Not true

Exercise #2

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Video Solution

Answer

Not true

Exercise #3

Given the parallelogram:AAABBBDDDCCC

Is this parallelogram a rhombus?

Video Solution

Answer

True

Exercise #4

Given the parallelogram:

AAABBBDDDCCC9999

Is this parallelogram a rhombus?

Video Solution

Answer

True

Exercise #5

Look at the parallelogram below:

AAABBBDDDCCC

The diagonals form 2 pairs of different angles at the center of the parallelogram.

Is the parallelogram a rhombus?

Video Solution

Answer

No.

Exercise #1

Look at the parallelogram below:

AAABBBDDDCCC

The diagonals form 90 degrees at the center of the parallelogram.

Is this parallelogram a rhombus?

Video Solution

Answer

Yes.

Exercise #2

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Video Solution

Answer

Yes

Exercise #3

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Video Solution

Answer

No