Quadrilateral Analysis: Testing Parallelogram Properties with Side Lengths 7, 6, 2, and 3

Parallelogram Properties with Unequal Side Lengths

Shown below is the quadrilateral ABCD.

AB = 7 and CD = 6.

BD = 2 and AC = 3.

AAABBBDDDCCC6327

Is the quadrilateral a parallelogram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:11 Let's find out if our shape is a parallelogram.
00:15 A parallelogram has two pairs. Each pair has equal and opposite sides.
00:21 Now, let's check the sides of our quadrilateral.
00:25 The opposite sides aren't equal, so it's not a parallelogram.
00:29 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Shown below is the quadrilateral ABCD.

AB = 7 and CD = 6.

BD = 2 and AC = 3.

AAABBBDDDCCC6327

Is the quadrilateral a parallelogram?

2

Step-by-step solution

To determine if the quadrilateral ABCDABCD is a parallelogram, we need to check if both pairs of opposite sides are equal in length.

  • Step 1: Compare opposite sides - We know AB=7AB = 7 and CD=6CD = 6. Since ABCDAB \neq CD, one pair of opposite sides is not equal.
  • Step 2: Check potential diagonal properties - The diagonals BD=2BD = 2 and AC=3AC = 3 are also not equal in length. In a parallelogram, diagonals bisect each other, so this is irrelevant as we don't have diagonal bisection condition due to lack of bisection evidence.

Since the condition for both pairs of opposite sides being equal is violated, quadrilateral ABCDABCD is not a parallelogram.

Given this analysis, the solution to the problem is: No.

3

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Parallelograms must have both pairs of opposite sides equal
  • Technique: Compare AB = 7 with CD = 6; since 7 ≠ 6, not parallel
  • Check: If one pair fails the equal test, it's not a parallelogram ✓

Common Mistakes

Avoid these frequent errors
  • Confusing diagonal lengths with side requirements
    Don't think diagonals being different (BD = 2, AC = 3) determines parallelogram status = wrong focus! Diagonal properties are separate from the basic definition. Always check if opposite sides are equal first - that's the fundamental requirement.

Practice Quiz

Test your knowledge with interactive questions

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

AAABBBDDDCCC134615

Is it possible to conclude that this quadrilateral is a parallelogram?

FAQ

Everything you need to know about this question

What exactly makes a shape a parallelogram?

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A quadrilateral is a parallelogram when both pairs of opposite sides are equal and parallel. In our problem, AB should equal CD, and BC should equal AD.

Why don't the diagonal lengths matter for this test?

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Diagonal lengths are properties of parallelograms but not the definition. We use side lengths to determine if it's a parallelogram first, then we can explore diagonal properties.

What if only one pair of opposite sides is equal?

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That's not enough! You need both pairs of opposite sides to be equal. If AB = CD but BC ≠ AD (or vice versa), it's not a parallelogram.

Could this quadrilateral be some other special shape?

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Possibly! Just because it's not a parallelogram doesn't mean it's not special. It could be a trapezoid or just a general quadrilateral, but we'd need more information to determine that.

How do I remember all the parallelogram properties?

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Start with the basic definition: opposite sides equal and parallel. Everything else (like diagonals bisecting each other) flows from this fundamental property!

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