Parallelogram Verification: Analysis of Quadrilateral with 100° and 80° Angles

Parallelogram Properties with Insufficient Angle Information

Given the quadrilateral ABCD where:

A=100° ∢A=100°

y C=80° ∢C=80°

AAABBBDDDCCC100°80°

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

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1

Understand the problem

Given the quadrilateral ABCD where:

A=100° ∢A=100°

y C=80° ∢C=80°

AAABBBDDDCCC100°80°

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

2

Step-by-step solution

A parallelogram is a quadrilateral whose two pairs of sides are parallel.

Since we know that angles A and C add up to 180 degrees, we know that AB is parallel to CD.

We have no way to prove if AC is parallel to BD since we have no data regarding angle B or angle D.

Therefore, the quadrilateral is not a parallelogram.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rule: Parallelograms need opposite sides parallel, not just one pair
  • Technique: Two angles totaling 180° proves one pair parallel: 100° + 80° = 180°
  • Check: Verify all four angles or opposite side relationships before concluding ✓

Common Mistakes

Avoid these frequent errors
  • Assuming one pair of parallel sides makes a parallelogram
    Don't conclude parallelogram from just angles A + C = 180° = one pair of parallel sides! This only proves AB || CD, but we need both pairs parallel. Always verify that opposite sides are parallel OR use other parallelogram properties.

Practice Quiz

Test your knowledge with interactive questions

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

AAABBBDDDCCC134615

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

FAQ

Everything you need to know about this question

Why isn't knowing two opposite angles enough to prove it's a parallelogram?

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A parallelogram needs both pairs of opposite sides to be parallel. When A+C=180° ∢A + ∢C = 180° , we only know that AB || CD. We still need to prove that AC || BD, but we don't know angles B or D!

What does it mean when two angles add up to 180°?

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When two angles on the same side of a transversal add up to 180°, it proves those lines are parallel. Here, angles A and C are co-interior angles, so 100° + 80° = 180° means AB || CD.

What information would I need to prove this is a parallelogram?

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You'd need any one of these:

  • All four angle measures
  • Two pairs of parallel sides
  • Two pairs of equal opposite sides
  • Diagonals that bisect each other

Could this quadrilateral still be a parallelogram even though we can't prove it?

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Yes! The quadrilateral might be a parallelogram, but we cannot conclude it definitively from the given information. We need more data to be certain.

What's the difference between 'possible' and 'provable' in geometry?

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Something is possible if it could be true, but provable means we have enough evidence to be certain. Here, it's possible this is a parallelogram, but not provable with just two angles.

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