Asked by Ian
Choose ALL answers that describe the polygon JKLM if m∠J=83∘, m∠K=97∘, m∠L=83∘, m∠M=97∘, JK ∥ LM, and KL ∥ MJ. Parallelogram, Quadrilateral, Rectangle, Rhombus, Square, Trapezoid.
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Answers: Parallelogram and Quadrilateral.
Reason: JK ∥ LM and KL ∥ MJ means both pairs of opposite sides are parallel, so JKLM is a parallelogram (hence a quadrilateral). The angles (83° and 97°) are consistent with a non‑rectangular parallelogram, so it is not a rectangle. No information is given about all sides being equal, so it is not necessarily a rhombus or square. Under the usual (exclusive) definition of trapezoid (exactly one pair of parallel sides) it is not a trapezoid.
Reason: JK ∥ LM and KL ∥ MJ means both pairs of opposite sides are parallel, so JKLM is a parallelogram (hence a quadrilateral). The angles (83° and 97°) are consistent with a non‑rectangular parallelogram, so it is not a rectangle. No information is given about all sides being equal, so it is not necessarily a rhombus or square. Under the usual (exclusive) definition of trapezoid (exactly one pair of parallel sides) it is not a trapezoid.
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