Shown below is the quadrilateral ABCD.
AB = 7 and CD = 6.
BD = 3 and AC = 4.
Is the quadrilateral a parallelogram?
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Shown below is the quadrilateral ABCD.
AB = 7 and CD = 6.
BD = 3 and AC = 4.
Is the quadrilateral a parallelogram?
To determine if a quadrilateral is a parallelogram, we need to check if both pairs of opposite sides are congruent. Given:
Check for opposite sides:
Since and are not equal, the condition for opposite side congruence in a parallelogram is violated.
Thus, the quadrilateral is not a parallelogram.
Therefore, 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?
Diagonal lengths alone don't determine parallelogram properties! You need to check opposite sides for congruence. Even if diagonals were equal, it wouldn't guarantee a parallelogram.
That's not enough! A parallelogram requires both pairs of opposite sides to be congruent. If AB = CD but AD ≠ BC, it's still not a parallelogram.
Not necessarily! If you can show that one pair of opposite sides is unequal, you immediately know it's not a parallelogram. In this case, is sufficient.
There are several methods: opposite sides parallel and congruent, opposite angles congruent, diagonals bisect each other, or one pair of sides both parallel and congruent.
Possibly! It could be a trapezoid (one pair of parallel sides) or just a general quadrilateral. But with the given information, we can definitively say it's not a parallelogram.
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