From a Parallelogram to a Rhombus - Examples, Exercises and Solutions

Question Types:
From a Parallelogram to a Rhombus: Determine whether the parallelogram is a rhombus

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.

parallel to the rectangle

Detailed explanation

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

Question 1

Given the parallelogram:AAABBBDDDCCC

Is this parallelogram a rhombus?

Question 2

Look at the parallelogram below:

AAABBBDDDCCC

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

Is this parallelogram a rhombus?

Question 3

AAABBBDDDCCC7575

Can the given parallelogram be considered a rhombus?

Question 4

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Question 5

Given the parallelogram:

AAABBBDDDCCC9999

Is this parallelogram a rhombus?

Examples with solutions for From a Parallelogram to a Rhombus

Exercise #1

Given the parallelogram:AAABBBDDDCCC

Is this parallelogram a rhombus?

Video Solution

Step-by-Step Solution

The definition of a rhombus is "a quadrilateral with all sides equal"

Therefore, the square in the diagram is indeed a rhombus

Thus, the correct answer is answer A.

Answer

True

Exercise #2

Look at the parallelogram below:

AAABBBDDDCCC

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

Is this parallelogram a rhombus?

Video Solution

Step-by-Step Solution

The parallelogram whose diagonals are perpendicular to each other (meaning the angle between them is 90° 90\degree ) is a rhombus, therefore the given parallelogram is a rhombus.

Therefore, the correct answer is answer A.

Answer

Yes.

Exercise #3

AAABBBDDDCCC7575

Can the given parallelogram be considered a rhombus?

Video Solution

Step-by-Step Solution

The definition of a rhombus is "a parallelogram with all equal sides", and since it is also a type of parallelogram, it is a parallelogram with one pair of adjacent and equal sides (since in a parallelogram opposite sides are equal)

In the parallelogram shown in the drawing, the adjacent sides are clearly not equal in length,

therefore the parallelogram shown in the drawing is not a rhombus.

Therefore the correct answer is answer B.

Answer

No

Exercise #4

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Video Solution

Answer

Not true

Exercise #5

Given the parallelogram:

AAABBBDDDCCC9999

Is this parallelogram a rhombus?

Video Solution

Answer

True

Question 1

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?

Question 2

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Question 3

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Exercise #6

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 #7

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Video Solution

Answer

Yes

Exercise #8

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Video Solution

Answer

No