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?
Given that a parallelogram is a quadrilateral whose two pairs of sides are parallel, and in the figure only two angles are given to us.
We do not have enough data to determine and prove whether angles C and B are equal to each other.
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 parallel, which means opposite angles must be equal and consecutive angles must be supplementary (add to 180°).
You need information about all four angles! Even if , angles B and C could be anything as long as the sum equals 360°. This isn't enough to guarantee parallelogram properties.
You'd need to show that opposite angles are equal: and , OR that consecutive angles are supplementary: .
Yes! It could be a trapezoid, kite, or irregular quadrilateral. Having doesn't eliminate other possibilities since we don't know angles B and C.
Always ask: "Do I have enough information to prove ALL the required properties?" For parallelograms, you need evidence about both pairs of opposite angles or sides, not just one pair.
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