Parallelogram Verification: Quadrilateral with Sides 15 and Diagonals 10

Q: Do equal diagonals mean it's a parallelogram?

No! Equal diagonals (AC = BD = 10) don't guarantee a parallelogram. You need opposite sides to be equal. Equal diagonals actually suggest it might be a rectangle or isosceles trapezoid.

Q: What information do I actually need to verify a parallelogram?

You need to check that both pairs of opposite sides are congruent: AB = CD and BC = AD. From the problem, we know AB = CD = 15, but we'd need BC and AD lengths too for complete verification.

Q: Is the given information enough to prove it's a parallelogram?

Not completely! We only know AB = CD = 15, which shows one pair of opposite sides are equal. We need information about BC and AD to fully prove it's a parallelogram.

Q: What other methods can prove a quadrilateral is a parallelogram?

Opposite sides parallel: AB || CD and BC || ADOpposite angles equal: ∠A = ∠C and ∠B = ∠DDiagonals bisect each other: They meet at their midpoints

Parallelogram Verification with Diagonal Measurements

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 15.

BD = 10 and AC = 10.

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 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 We found 2 pairs of equal opposite sides, therefore it's a parallelogram

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 = 15 and CD = 15.

BD = 10 and AC = 10.

Is the quadrilateral a parallelogram?

Step-by-step solution

To determine if quadrilateral ABCD is a parallelogram, we need to use the property that for a quadrilateral to be a parallelogram, both pairs of opposite sides must be congruent.

The given measurements are:

AB = 15
CD = 15
BD = 10
AC = 10

Check the congruency of opposite sides:

AB and CD are opposite sides: $AB = CD = 15$
For diagonals AC and BD, their lengths do not affect our conclusion concerning sides, though we see diagonals lengths as equal, this extra fact isn't of consequence in this specific theorem application.

Since both pairs of sides AB and CD are equal, and as per the theorem that if opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram, ABCD is a parallelogram.

Therefore, we determine that the solution to the problem is Yes.

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic

Definition: Parallelogram has opposite sides equal and parallel
Technique: Check AB = CD (15) and BC = AD
Check: Verify both pairs of opposite sides are congruent ✓

Common Mistakes

Avoid these frequent errors

Using diagonal lengths to determine side properties
Don't use diagonal measurements (AC = 10, BD = 10) to conclude opposite sides are equal = wrong reasoning! Equal diagonals don't guarantee a parallelogram. Always check that opposite sides AB = CD and BC = AD are congruent.

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

Do equal diagonals mean it's a parallelogram?

No! Equal diagonals (AC = BD = 10) don't guarantee a parallelogram. You need opposite sides to be equal. Equal diagonals actually suggest it might be a rectangle or isosceles trapezoid.

What information do I actually need to verify a parallelogram?

You need to check that both pairs of opposite sides are congruent: AB = CD and BC = AD. From the problem, we know AB = CD = 15, but we'd need BC and AD lengths too for complete verification.

Is the given information enough to prove it's a parallelogram?

Not completely! We only know AB = CD = 15, which shows one pair of opposite sides are equal. We need information about BC and AD to fully prove it's a parallelogram.

What other methods can prove a quadrilateral is a parallelogram?

Opposite sides parallel: AB || CD and BC || AD
Opposite angles equal: ∠A = ∠C and ∠B = ∠D
Diagonals bisect each other: They meet at their midpoints

Why does the explanation say the answer is 'Yes'?

The explanation assumes we have enough information, but it's actually incomplete. In a real test, you'd need all four side lengths or other properties to definitively prove it's a parallelogram.

🌟 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

Parallelogram Verification: Quadrilateral with Sides 15 and Diagonals 10

Parallelogram Verification with Diagonal Measurements

❤️ 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

Do equal diagonals mean it's a parallelogram?

What information do I actually need to verify a parallelogram?

Is the given information enough to prove it's a parallelogram?

What other methods can prove a quadrilateral is a parallelogram?

Why does the explanation say the answer is 'Yes'?

🌟 Unlock Your Math Potential

More Questions

Identifying a Parallelogram

Verify Parallelogram Properties: Quadrilateral ABCD with Sides 10 and 8

Quadrilateral Analysis: Testing Parallelogram Properties with Sides 20 and 8

Quadrilateral Analysis: Is ABCD with Sides 7,6 and Diagonals 3,4 a Parallelogram?

Parallelogram Identification: Quadrilateral with Sides 6-6-4-4