Shown below is the quadrilateral ABCD.
AB = 7 and CD = 6.
BD = 2 and AC = 3.
Is the quadrilateral a parallelogram?
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Shown below is the quadrilateral ABCD.
AB = 7 and CD = 6.
BD = 2 and AC = 3.
Is the quadrilateral a parallelogram?
To determine if the quadrilateral is a parallelogram, we need to check if both pairs of opposite sides are equal in length.
Since the condition for both pairs of opposite sides being equal is violated, quadrilateral is not a parallelogram.
Given this analysis, the solution to the problem is: No.
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 quadrilateral is a parallelogram when both pairs of opposite sides are equal and parallel. In our problem, AB should equal CD, and BC should equal AD.
Diagonal lengths are properties of parallelograms but not the definition. We use side lengths to determine if it's a parallelogram first, then we can explore diagonal properties.
That's not enough! You need both pairs of opposite sides to be equal. If AB = CD but BC ≠ AD (or vice versa), it's not a parallelogram.
Possibly! Just because it's not a parallelogram doesn't mean it's not special. It could be a trapezoid or just a general quadrilateral, but we'd need more information to determine that.
Start with the basic definition: opposite sides equal and parallel. Everything else (like diagonals bisecting each other) flows from this fundamental property!
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