Question

choose all answers that describe the polygon ( i j k l ) if ( overline{i j} cong overline{j k} cong overline{k l} cong overline{l i}, m angle i=95^{circ}, m angle j=85^{circ} ), ( m angle k=95^{circ} ), and ( m angle l=85^{circ} ).

Explanation:

Step1: Determine the type of polygon

Since \(IJKL\) has \(4\) sides, it is a quadrilateral.

Step2: Check for parallelogram properties

In a parallelogram, opposite angles are equal. Here, \(\angle I = 95^{\circ}\) and \(\angle K=95^{\circ}\), \(\angle J = 85^{\circ}\) and \(\angle L = 85^{\circ}\). So it is a parallelogram.

Step3: Check for rhombus properties

In a rhombus, all sides are equal (\(\overline{IJ}\cong\overline{JK}\cong\overline{KL}\cong\overline{LI}\)) and it is a parallelogram. So it is a rhombus.

Step4: Check for rectangle and square properties

A rectangle has all angles equal to \(90^{\circ}\). A square has all angles equal to \(90^{\circ}\) and all sides equal. Since angles are \(95^{\circ}\) and \(85^{\circ}\), it is not a rectangle or square.

Step5: Check for trapezoid properties

A trapezoid has only one pair of parallel sides. But as it is a parallelogram (two pairs of parallel sides), it is not a trapezoid.

Answer:

• Quadrilateral
• Parallelogram
• Rhombus