Parallelogram Analysis: Quadrilateral with Sides 7, 8, and 11 Units

Q: Why can't this be a parallelogram if one pair of opposite sides are equal?

A parallelogram requires both pairs of opposite sides to be equal! In this quadrilateral, AB = CD = 11, but BC = 7 and AD = 8. Since 7 ≠ 8, it fails the parallelogram test.

Q: Could this shape be any other type of quadrilateral?

Yes! This could be a trapezoid (if AB is parallel to CD) or just a general quadrilateral. The key is that it's not a parallelogram due to unequal opposite sides.

Q: How do I remember the parallelogram properties?

Think "Opposite sides: Parallel AND Equal". Both conditions must be true! Use the acronym OPAE: Opposite sides are Parallel And Equal.

Parallelogram Properties with Opposite Side Analysis

Below is a quadrilateral:

Is it possible that it is a parallelogram?

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Step-by-step written solution

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Understand the problem

Below is a quadrilateral:

Is it possible that it is a parallelogram?

Step-by-step solution

According to the properties of a parallelogram, any two opposite sides will be equal to each other.

From the data, it can be observed that only one pair of opposite sides are equal and therefore the quadrilateral is not a parallelogram.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: In parallelograms, opposite sides must be equal in length
Method: Compare AB with CD and BC with AD: 11=11 ✓, but 7≠8
Verification: Check both pairs of opposite sides are equal ✓

Common Mistakes

Avoid these frequent errors

Checking only one pair of opposite sides
Don't assume it's a parallelogram if just one pair of opposite sides are equal = wrong conclusion! This ignores the requirement that ALL opposite sides must be equal. Always verify that BOTH pairs of opposite sides have equal lengths.

Practice Quiz

Test your knowledge with interactive questions

It is possible to draw a quadrilateral that is not a rectangle and that has two equal opposite sides?

FAQ

Everything you need to know about this question

Why can't this be a parallelogram if one pair of opposite sides are equal?

A parallelogram requires both pairs of opposite sides to be equal! In this quadrilateral, AB = CD = 11, but BC = 7 and AD = 8. Since 7 ≠ 8, it fails the parallelogram test.

What if I only look at the parallel sides?

Being parallel isn't enough! Even if two sides are parallel, you need both pairs of opposite sides to be parallel AND equal for a true parallelogram.

Could this shape be any other type of quadrilateral?

Yes! This could be a trapezoid (if AB is parallel to CD) or just a general quadrilateral. The key is that it's not a parallelogram due to unequal opposite sides.

How do I remember the parallelogram properties?

Think "Opposite sides: Parallel AND Equal". Both conditions must be true! Use the acronym OPAE: Opposite sides are Parallel And Equal.

What's the easiest way to check if a quadrilateral is a parallelogram?

Compare the lengths! List opposite sides in pairs:

Side 1 vs Side 3
Side 2 vs Side 4

If both pairs are equal, it could be a parallelogram (you'd also need to verify they're parallel).

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