Question

choose all answers that describe the polygon lmno if lm = 10, mn = 10, no = 10, ol = 10, and m∠l = m∠m = m∠n = m∠o. answer attempt 1 out of 1 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Analyze the number of sides

A polygon with 4 sides is a quadrilateral. Since \(LMNO\) has 4 sides (\(LM\), \(MN\), \(NO\), \(OL\)), it is a quadrilateral.

Step2: Check for parallelogram properties

In a parallelogram, opposite sides are equal. Here \(LM = NO = 10\) and \(MN=OL = 10\). Also, in a parallelogram, opposite angles are equal. Given \(m\angle L=m\angle N\) and \(m\angle M = m\angle O\) (since \(m\angle L=m\angle M=m\angle N=m\angle O\)), so it is a parallelogram.

Step3: Check for rhombus properties

A rhombus is a parallelogram with all sides equal. Since \(LM = MN=NO = OL = 10\), it is a rhombus.

Step4: Check for rectangle properties

A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\). If \(m\angle L=m\angle M=m\angle N=m\angle O\), then \(m\angle L=m\angle M=m\angle N=m\angle O=\frac{360^{\circ}}{4}=90^{\circ}\). So it is a rectangle.

Step5: Check for square properties

A square is a rectangle and a rhombus (all sides equal and all angles \(90^{\circ}\)). Since it is a rectangle (all angles \(90^{\circ}\)) and a rhombus (all sides equal), it is a square.

Step6: Analyze trapezoid

A trapezoid has at least one pair of parallel sides. But a trapezoid does not satisfy the properties of having all sides equal and all angles equal. So it is not a trapezoid.

Answer:

Parallelogram, Quadrilateral, Rectangle, Rhombus, Square