Quadrilateral Analysis: Testing Parallelogram Properties with Sides 20 and 8

Q: Why can't I use the diagonal lengths to prove it's a parallelogram?

Diagonal lengths BD = 8 and AC = 8 tell us about rectangle properties, not parallelogram properties. For parallelograms, we need opposite sides to be equal, not diagonals.

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

Yes! One pair being equal isn't enough. You need AB = CD AND BC = AD to confirm it's a parallelogram using the opposite sides theorem.

Q: What if the problem doesn't give me all four side lengths?

Look for other clues! The diagram might show parallel marks or congruent markings. Sometimes the construction itself implies the missing information, like in this problem.

Q: What does 'implied by construction' mean in the explanation?

Sometimes the way a figure is drawn or described gives us information not explicitly stated. Here, the diagram suggests BC = AD even though we're only told about AB and CD.

Parallelogram Testing with Opposite Side Properties

Shown below is the quadrilateral ABCD.

AB = 20 and CD = 20.

BD = 8 and AC = 8.

Is the quadrilateral a parallelogram?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the square a parallelogram?

00:03 One pair of opposite sides are equal according to the given data

00:08 Second pair of opposite sides are equal according to the given data

00:11 A parallelogram is a quadrilateral with 2 pairs of equal opposite sides

00:14 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

Shown below is the quadrilateral ABCD.

AB = 20 and CD = 20.

BD = 8 and AC = 8.

Is the quadrilateral a parallelogram?

Step-by-step solution

To determine if quadrilateral ABCD is a parallelogram, we can use the property of parallelograms that states if both pairs of opposite sides are congruent, the quadrilateral is a parallelogram.

Given:

$AB = 20$
$CD = 20$
$BD = 8$
$AC = 8$

Step 1: Identify opposite sides $AB$ and $CD$ .

Both sides $AB$ and $CD$ are given to be 20. Thus, they are congruent.

Since both pairs of opposite sides $AB$ and $CD$ are equal (and it is implied that $AD = BC$ by construction shown), we utilize the theorem for parallelograms:

If both pairs of opposite sides are congruent, it confirms that the quadrilateral is a parallelogram.

Therefore, based on this property, quadrilateral ABCD is indeed a parallelogram.

The final answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Two pairs of congruent opposite sides create a parallelogram
Technique: Compare $AB = CD = 20$ and verify second pair
Check: Both opposite side pairs must be equal for parallelogram confirmation ✓

Common Mistakes

Avoid these frequent errors

Confusing diagonals with sides for parallelogram test
Don't use diagonal lengths BD = 8 and AC = 8 to prove parallelogram properties = wrong conclusion! Diagonal equality proves rectangle, not parallelogram. Always compare opposite SIDES (AB with CD, BC with AD) for parallelogram tests.

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 can't I use the diagonal lengths to prove it's a parallelogram?

Diagonal lengths BD = 8 and AC = 8 tell us about rectangle properties, not parallelogram properties. For parallelograms, we need opposite sides to be equal, not diagonals.

Do I need both pairs of opposite sides to be equal?

Yes! One pair being equal isn't enough. You need AB = CD AND BC = AD to confirm it's a parallelogram using the opposite sides theorem.

What if the problem doesn't give me all four side lengths?

Look for other clues! The diagram might show parallel marks or congruent markings. Sometimes the construction itself implies the missing information, like in this problem.

Are there other ways to prove a quadrilateral is a parallelogram?

Yes! You can also prove it by showing:

Both pairs of opposite sides are parallel
One pair of sides is both parallel and congruent
Opposite angles are congruent

What does 'implied by construction' mean in the explanation?

Sometimes the way a figure is drawn or described gives us information not explicitly stated. Here, the diagram suggests BC = AD even though we're only told about AB and CD.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram for Ninth Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Quadrilateral Analysis: Testing Parallelogram Properties with Sides 20 and 8

Parallelogram Testing with Opposite Side Properties

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I use the diagonal lengths to prove it's a parallelogram?

Do I need both pairs of opposite sides to be equal?

What if the problem doesn't give me all four side lengths?

Are there other ways to prove a quadrilateral is a parallelogram?

What does 'implied by construction' mean in the explanation?

🌟 Unlock Your Math Potential

More Questions

Identifying a Parallelogram

Parallelogram Verification: Analyzing a Quadrilateral with Sides 15 and 13

Parallelogram Verification: Quadrilateral with Equal Sides (11) and Diagonals (4)

Verify Parallelogram Properties: Quadrilateral ABCD with Sides 10 and 8

Parallelogram Verification: Quadrilateral with Sides 15 and Diagonals 10