Given the quadrilateral ABCD where:
y
Is it possible to conclude that this quadrilateral is a parallelogram?
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Given the quadrilateral ABCD where:
y
Is it possible to conclude that this quadrilateral is a parallelogram?
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.
No
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?
A parallelogram needs both pairs of opposite sides to be parallel. When , we only know that AB || CD. We still need to prove that AC || BD, but we don't know angles B or D!
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.
You'd need any one of these:
Yes! The quadrilateral might be a parallelogram, but we cannot conclude it definitively from the given information. We need more data to be certain.
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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