Parallelogram with Sides 5 and 7: Determine if it's a Rhombus

Rhombus Identification with Unequal Sides

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Can the given parallelogram be considered a rhombus?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the parallelogram a rhombus?
00:03 In a parallelogram, opposite sides are parallel
00:12 Let's check if adjacent sides are equal in the parallelogram
00:20 The sides are not equal, therefore the parallelogram is not a rhombus
00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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Can the given parallelogram be considered a rhombus?

2

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.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: A rhombus is a parallelogram with all four sides equal
  • Technique: Check if adjacent sides match: side 5 ≠ side 7
  • Check: If any two sides are different lengths, it's not a rhombus ✓

Common Mistakes

Avoid these frequent errors
  • Thinking any parallelogram is a rhombus
    Don't assume that because a shape is a parallelogram, it must be a rhombus = wrong classification! All rhombuses are parallelograms, but not all parallelograms are rhombuses. Always check that all four sides are equal before calling it a rhombus.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

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Is this parallelogram a rhombus?

FAQ

Everything you need to know about this question

What's the difference between a parallelogram and a rhombus?

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A parallelogram has opposite sides that are parallel and equal. A rhombus is a special parallelogram where all four sides are equal length!

Can a parallelogram with sides 5 and 7 ever be a rhombus?

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No, never! For a shape to be a rhombus, all sides must be the same length. Since 5 ≠ 7, this parallelogram cannot be a rhombus.

What if the parallelogram had all sides equal to 5?

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Then it would be a rhombus! When all four sides of a parallelogram are equal, it automatically becomes a rhombus.

Are there other special parallelograms besides rhombuses?

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Yes! Rectangles are parallelograms with four right angles, and squares are parallelograms that are both rectangles AND rhombuses (equal sides + right angles).

How do I remember the definition of a rhombus?

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Think "Rhombus = Parallel + Equal" - it has the parallel sides of a parallelogram plus all sides are equal length!

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