Parallelogram to Rhombus: Geometric Shape Classification Analysis

Quadrilateral Classification with Side Length Properties

AAABBBDDDCCCCan the above 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
00:10 Sides are equal according to the given
00:15 A parallelogram with equal adjacent sides is a rhombus
00:19 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

AAABBBDDDCCCCan the above parallelogram be considered a rhombus?

2

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.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Definition: Rhombus requires all four sides to be equal in length
  • Technique: Check if parallelogram has equal adjacent sides AB = BC
  • Verification: Confirm all sides match: AB = BC = CD = DA ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all parallelograms are rhombuses
    Don't automatically call every parallelogram a rhombus = wrong classification! A parallelogram only has opposite sides equal, not all four sides. Always check if all four sides are equal before calling it a rhombus.

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 parallelogram and a rhombus?

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A parallelogram has opposite sides equal and parallel. A rhombus has all four sides equal AND parallel. Every rhombus is a parallelogram, but not every parallelogram is a rhombus!

How can I tell if this parallelogram is actually a rhombus?

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Look at the diagram carefully! If all sides appear to be the same length, then it's a rhombus. In this case, the shape looks like it has equal sides, making it both a parallelogram AND a rhombus.

Can a square be considered a rhombus?

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Yes! A square is a special type of rhombus where all sides are equal AND all angles are 90°. So every square is automatically a rhombus (and also a parallelogram).

What if the sides look equal but I'm not sure?

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In geometry problems, if the diagram shows equal side markings or appears to have equal sides, you can usually assume they are equal. Trust the visual clues in the diagram!

Are there other special parallelograms besides rhombuses?

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Yes! Rectangles are parallelograms with all right angles, and squares are parallelograms that are both rectangles AND rhombuses. Each has special properties!

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