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

Understanding From a Parallelogram to a Rhombus

Complete explanation with examples

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

Practice From a Parallelogram to a Rhombus

Test your knowledge with 2 quizzes

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

Examples with solutions for From a Parallelogram to a Rhombus

Step-by-step solutions included
Exercise #1

AAABBBDDDCCCCan the above parallelogram be considered a rhombus?

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

Video Solution
Exercise #2

AAABBBDDDCCC7575

Can the given parallelogram be considered a rhombus?

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

Video Solution
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?

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.

Video Solution
Exercise #4

Given the parallelogram:

AAABBBDDDCCC9999

Is this parallelogram a rhombus?

Step-by-Step Solution

Answer:

True

Video Solution
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?

Step-by-Step Solution

Answer:

No.

Video Solution

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