Verify Parallelogram Properties: Quadrilateral ABCD with Sides 10 and 8

Q: Why don't the diagonals matter for determining if it's a parallelogram?

While parallelograms do have special diagonal properties, equal opposite sides is the primary test. The diagonals bisect each other in parallelograms, but just knowing their lengths isn't enough to determine the shape.

Q: Do I need to check both pairs of opposite sides?

Technically yes, but if one pair of opposite sides is unequal (like AB ≠ CD), you can immediately conclude it's not a parallelogram without checking the other pair!

Q: Could this quadrilateral be some other special shape?

Yes! It could be a trapezoid (one pair of parallel sides) or just a general quadrilateral. But since opposite sides aren't equal, it definitely cannot be a parallelogram, rectangle, rhombus, or square.

Q: How do I remember the parallelogram properties?

Think "Parallel-ogram" = parallel sides! The key properties are: Opposite sides are equal and parallelOpposite angles are equalDiagonals bisect each other

Parallelogram Properties with Unequal Opposite Sides

Look at the quadrilateral ABCD shown below.

AB = 10 and CD = 8.

BD = 7 and AC = 6.

Is the quadrilateral a parallelogram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the quadrilateral a parallelogram?

00:03 A parallelogram is a quadrilateral with 2 pairs of equal opposite sides

00:07 Let's check the sides of our quadrilateral

00:11 Opposite sides are not equal, therefore it's not a parallelogram

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the quadrilateral ABCD shown below.

AB = 10 and CD = 8.

BD = 7 and AC = 6.

Is the quadrilateral a parallelogram?

Step-by-step solution

The problem requires us to determine if the quadrilateral ABCD is a parallelogram based on given side and diagonal lengths.

To determine if ABCD is a parallelogram, we check if both pairs of opposite sides are equal:

For sides $AB$ and $CD$ , the lengths given are $AB = 10$ and $CD = 8$ . These are not equal, hence the first condition $AB = CD$ for a parallelogram is not met.
We also need to check if the other pair of opposite sides satisfies $AD = BC$ . However, without additional information, like equality of the other pair of sides, we cannot verify $AD = BC$ using the given lengths alone.

Since one necessary condition for ABCD to be a parallelogram is broken (i.e., $AB \neq CD$ ), we can conclude that quadrilateral ABCD is not a parallelogram.

Therefore, the correct answer is No.

Final Answer

No.

Key Points to Remember

Essential concepts to master this topic

Parallelogram Rule: Both pairs of opposite sides must be equal
Check Technique: Compare AB = 10 with CD = 8 (not equal)
Verification: If any opposite side pair differs, quadrilateral is not parallelogram ✓

Common Mistakes

Avoid these frequent errors

Focusing only on diagonal lengths instead of side lengths
Don't use diagonal lengths BD = 7 and AC = 6 to determine if it's a parallelogram = wrong approach! Diagonals don't determine parallelogram properties directly. Always check if opposite sides are equal first: AB vs CD and AD vs BC.

Practice Quiz

Test your knowledge with interactive questions

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

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

FAQ

Everything you need to know about this question

Why don't the diagonals matter for determining if it's a parallelogram?

While parallelograms do have special diagonal properties, equal opposite sides is the primary test. The diagonals bisect each other in parallelograms, but just knowing their lengths isn't enough to determine the shape.

Do I need to check both pairs of opposite sides?

Technically yes, but if one pair of opposite sides is unequal (like AB ≠ CD), you can immediately conclude it's not a parallelogram without checking the other pair!

What if I can't see all the side lengths in the diagram?

Use the given information strategically. In this problem, we're told AB = 10 and CD = 8, which is enough since these are opposite sides and they're not equal.

Could this quadrilateral be some other special shape?

Yes! It could be a trapezoid (one pair of parallel sides) or just a general quadrilateral. But since opposite sides aren't equal, it definitely cannot be a parallelogram, rectangle, rhombus, or square.

How do I remember the parallelogram properties?

Think "Parallel-ogram" = parallel sides! The key properties are:

Opposite sides are equal and parallel
Opposite angles are equal
Diagonals bisect each other

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