Question

1. choose all answers that describe the polygon j k l m if j k = l m, k l = m j, m ∠ j = 90 ^ { circ }, m ∠ k = 90 ^ { circ }, m ∠ l = 90 ^ { circ }, and m ∠ m = 90 ^ { circ }.

□ parallelogram □ quadrilateral □ rectangle
□ rhombus □ square

Explanation:

Step1: Analyze the properties of a quadrilateral

A quadrilateral is a four - sided polygon. Since \(JKLM\) has four sides, it is a quadrilateral.

Step2: Analyze the properties of a parallelogram

In a parallelogram, opposite sides are equal. Here \(JK = LM\) and \(KL = MJ\), so it satisfies the property of a parallelogram.

Step3: Analyze the properties of a rectangle

A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). Since \(m\angle J=m\angle K = m\angle L=m\angle M = 90^{\circ}\), it is a rectangle.

Step4: Analyze the properties of a square

A square is a rectangle with all sides equal. Given \(JK = LM\), \(KL = MJ\) and all angles \(90^{\circ}\), if \(JK = KL\) (implied by the equal - side relationships in the given problem structure as \(JK = LM\), \(KL = MJ\) and in a parallelogram \(JK\parallel LM\), \(KL\parallel MJ\)), then it is a square.

Step5: Analyze the properties of a rhombus

A rhombus is a parallelogram with all sides equal. Since \(JK = LM\), \(KL = MJ\) and in a parallelogram \(JK\parallel LM\), \(KL\parallel MJ\), if all sides are equal (which is consistent with the given equal - side conditions when considering the relationships in a parallelogram), and with right angles (a rhombus with right angles is a square, and a square is a special case of a rhombus).

Answer:

Parallelogram, Quadrilateral, Rectangle, Square, Rhombus