Quadrilateral Analysis: Testing Parallelogram Properties with Sides 10, 8 and Diagonals 2, 4

Q: Why don't the diagonal lengths matter here?

For basic parallelogram identification, opposite sides equality is the primary test. While parallelograms do have special diagonal properties (they bisect each other), you need equal opposite sides first!

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

Yes, absolutely! A parallelogram requires both pairs of opposite sides to be equal: AB = CD and AD = BC. If even one pair fails, it's not a parallelogram.

Q: What if only one pair of opposite sides is equal?

That would make it a trapezoid (one pair of parallel sides), not a parallelogram. Parallelograms need both pairs of opposite sides equal and parallel.

Q: Since AB = 10 and CD = 8, can this ever be a parallelogram?

No, never! Since 10 ≠ 8, these opposite sides aren't equal. No matter what the other measurements are, this quadrilateral cannot be a parallelogram.

Q: What should I check first when testing for parallelograms?

Always start with opposite sides equality! It's the most straightforward test. If AB ≠ CD or AD ≠ BC, you immediately know it's not a parallelogram.

Parallelogram Properties with Opposite Sides

Below is the quadrilateral ABCD.

AB = 10 and CD = 8.

BD = 2 and AC = 4.

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, according to the given data

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

00:16 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

Below is the quadrilateral ABCD.

AB = 10 and CD = 8.

BD = 2 and AC = 4.

Is the quadrilateral a parallelogram?

Step-by-step solution

To determine if quadrilateral $ABCD$ is a parallelogram, we apply the condition that a parallelogram has both pairs of opposite sides congruent.

We are given:

Side $AB = 10$ .
Side $CD = 8$ .

To be a parallelogram, not only should $AB = CD$ , but $AD$ should be equal to $BC$ . However, the provided lengths don't satisfy this condition.

No further information is presented about the length equality of sides $AD$ and $BC$ , nor do provided diagonals imply certain conditions towards opposite sides equality.

Since $AB \neq CD$ , we immediately conclude the quadrilateral fails to meet the requirement of having both pairs of opposite sides equal as needed for it to be a parallelogram.

Therefore, the quadrilateral $ABCD$ is not a parallelogram.

Conclusion: No

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Parallelograms require both pairs of opposite sides equal
Technique: Check $AB = CD$ and $AD = BC$ : here 10 ≠ 8
Check: If any pair of opposite sides unequal, not parallelogram ✓

Common Mistakes

Avoid these frequent errors

Assuming diagonal information determines parallelogram status
Don't think diagonals BD = 2 and AC = 4 matter for basic parallelogram test = wrong focus! While diagonals have special properties in parallelograms, the fundamental requirement is opposite sides equality. Always check if AB = CD and AD = BC first.

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 diagonal lengths matter here?

For basic parallelogram identification, opposite sides equality is the primary test. While parallelograms do have special diagonal properties (they bisect each other), you need equal opposite sides first!

Do I need to check both pairs of opposite sides?

Yes, absolutely! A parallelogram requires both pairs of opposite sides to be equal: AB = CD and AD = BC. If even one pair fails, it's not a parallelogram.

What if only one pair of opposite sides is equal?

That would make it a trapezoid (one pair of parallel sides), not a parallelogram. Parallelograms need both pairs of opposite sides equal and parallel.

Since AB = 10 and CD = 8, can this ever be a parallelogram?

No, never! Since 10 ≠ 8, these opposite sides aren't equal. No matter what the other measurements are, this quadrilateral cannot be a parallelogram.

Are there other ways to prove something is a parallelogram?

Yes! You can also prove it by showing:

Both pairs of opposite sides are parallel
Diagonals bisect each other
One pair of sides is both equal and parallel

What should I check first when testing for parallelograms?

Always start with opposite sides equality! It's the most straightforward test. If AB ≠ CD or AD ≠ BC, you immediately know it's not a parallelogram.

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