Parallelogram Verification: Analyzing a Quadrilateral with Sides 15 and 13

Parallelogram Verification with Unequal Opposite Sides

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?

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1

Understand the problem

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?

2

Step-by-step solution

According to the properties of a parallelogram, each pair of opposite sides are parallel and equal to each other.

Since the data shows that each pair of sides are not equal to each other, the quadrilateral is not a parallelogram.

1513 15\ne13

46 4\ne6

3

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic
  • Parallelogram Property: Opposite sides must be equal and parallel
  • Method: Compare opposite sides AB = 15 vs CD = 13
  • Verification: Since 1513 15 \ne 13 and 46 4 \ne 6 , not a parallelogram ✓

Common Mistakes

Avoid these frequent errors
  • Focusing only on side lengths without checking opposite pairs
    Don't just look at all four measurements randomly = missing the key relationship! This ignores which sides are actually opposite to each other. Always identify opposite sides first, then check if AB equals CD and if AC equals BD.

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

Which sides are opposite in quadrilateral ABCD?

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In quadrilateral ABCD, the opposite sides are: AB opposite to CD, and BC opposite to AD. Think of it like corners of a rectangle - sides that don't share a vertex are opposite!

What if only one pair of opposite sides is equal?

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That's not enough for a parallelogram! You need both pairs of opposite sides to be equal and parallel. One pair being equal might make it a trapezoid instead.

Do the diagonal lengths matter for parallelograms?

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The diagonals AC = 4 and BD = 6 are given information, but for basic parallelogram verification, we focus on opposite sides being equal. Diagonals help with other properties!

Could this quadrilateral be some other special shape?

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Possibly! Even though it's not a parallelogram, it could be a trapezoid (one pair of parallel sides) or just a general quadrilateral. We'd need more information about angles or parallel relationships.

What if I mixed up which sides are opposite?

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Great question! Always trace around the quadrilateral in order: A→B→C→D→A. Then AB is opposite to CD, and BC is opposite to AD. Drawing arrows can help visualize this!

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