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.

Detailed explanation

Suggested Topics to Practice in Advance

  1. Rhombus, kite, or diamond?
  2. Diagonals of a Rhombus
  3. The Area of a Rhombus
  4. How do we calculate the area of complex shapes?

Practice From a Parallelogram to a Rhombus

Question 1

AAABBBDDDCCCCan the above parallelogram be considered a rhombus?

Question 2

AAABBBDDDCCC7575

Can the given parallelogram be considered a rhombus?

Question 3

Look at the parallelogram below:

AAABBBDDDCCC

If the diagonals cross at 90 degree angles at the center of the parallelogram.

Is this parallelogram considered a rhombus?

Question 4

Given the parallelogram:

AAABBBDDDCCC9999

Is this parallelogram a rhombus?

Question 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?

Examples with solutions for From a Parallelogram to a Rhombus

Exercise #1

AAABBBDDDCCCCan the above parallelogram be considered a rhombus?

Video Solution

Step-by-Step Solution

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

Therefore, the square in the diagram is indeed a rhombus

Thus, the correct answer is answer A.

Answer

True

Exercise #2

AAABBBDDDCCC7575

Can the given parallelogram be considered a rhombus?

Video Solution

Step-by-Step Solution

The definition of a rhombus is "a parallelogram with equal sides"

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

Therefore the parallelogram shown in the drawing cannot be considered a rhombus.

Therefore the correct answer is answer B.

Answer

No

Exercise #3

Look at the parallelogram below:

AAABBBDDDCCC

If the diagonals cross at 90 degree angles at the center of the parallelogram.

Is this parallelogram considered 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 #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.

Question 1

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Question 2

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Is this parallelogram necessarily a rhombus?

Question 3

AAABBBDDDCCC

Is this parallelogram necessarily a rhombus?

Exercise #6

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Video Solution

Answer

Not true

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