Perpendicular Diagonals in a Parallelogram: Is it a Rhombus?

Rhombus Properties with Perpendicular Diagonals

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?

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1

Understand the problem

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?

2

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.

3

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic
  • Property: Rhombus has perpendicular diagonals that bisect each other
  • Identification: If parallelogram diagonals meet at 90° 90° , it's a rhombus
  • Verification: Check that all four sides are equal lengths ✓

Common Mistakes

Avoid these frequent errors
  • Confusing rhombus with square requirements
    Don't assume a rhombus must have 90° angles at vertices = wrong classification! Perpendicular diagonals don't create right angles at corners. Always remember: rhombus needs equal sides and perpendicular diagonals, not corner right angles.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

AAABBBDDDCCC149149

Is this parallelogram a rhombus?

FAQ

Everything you need to know about this question

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

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A rhombus has all equal sides and perpendicular diagonals, but corner angles can be any measure. A square is a special rhombus where all corner angles are also 90° 90° .

Do all parallelograms with perpendicular diagonals become rhombuses?

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Yes! If a parallelogram has perpendicular diagonals, it must be a rhombus. This is a guaranteed property that always works both ways.

How can I tell if diagonals are really perpendicular?

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Look for the right angle symbol where diagonals cross, or check if the problem states they meet at 90° 90° . In this problem, it clearly says "90 degree angles at the center."

What other properties does a rhombus have?

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  • All sides are equal length
  • Opposite angles are equal
  • Diagonals bisect each other at right angles
  • Diagonals bisect the vertex angles

Can a rectangle be a rhombus too?

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Only if it's a square! A regular rectangle has perpendicular sides but not perpendicular diagonals, so it's not a rhombus unless all sides are equal.

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