Question

given the information marked on the figures below, classify each quadrilateral as a \parallelogram\ or
ot necessarily a parallelogram.\ note that each figure is drawn like a parallelogram, but you should not rely on how the figure is drawn in determining your answers. if necessary, you may learn what the markings on a figure indicate.

Explanation:

Step1: Recall parallelogram properties

A parallelogram has opposite - sides parallel and equal, opposite angles equal, and diagonals bisecting each other.

Step2: Analyze the first figure

If the markings show that opposite angles are equal, by the property of parallelograms (a quadrilateral with opposite angles equal is a parallelogram), it is a parallelogram.

Step3: Analyze the second figure

If the diagonals are marked as bisecting each other (the equal - length segments on the diagonals), by the property that a quadrilateral with diagonals bisecting each other is a parallelogram, it is a parallelogram.

Step4: Analyze the third figure

If the markings show that opposite sides are parallel and equal (the equal - length segments and parallel - line markings), by the definition of a parallelogram (a quadrilateral with two pairs of opposite sides parallel), it is a parallelogram.

Step5: Analyze the fourth figure

If the markings show that one pair of opposite sides is parallel and equal, by the property that a quadrilateral with one pair of opposite sides parallel and equal is a parallelogram, it is a parallelogram.

Answer:

The first figure: Parallelogram
The second figure: Parallelogram
The third figure: Parallelogram
The fourth figure: Parallelogram