parallelogram not necessarily a parallelogram parallelogram not necessarily a parallelogram parallelogram…

Explanation:

Step1: Recall parallelogram properties

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

Step2: Analyze first figure

In the first figure with quadrilateral (ABCD), just having (\angle BAC=\angle ACD) only shows that (AB\parallel CD) (alternate - interior angles are equal). We don't know about the other pair of sides, so it is not necessarily a parallelogram.

Step3: Analyze second figure

In the second figure with quadrilateral (KLMN), having four right - angles makes it a rectangle (a special type of parallelogram). Since a rectangle is a parallelogram, it is a parallelogram.

Step4: Analyze third figure

In the third figure with quadrilateral (PQRS), having (PQ = SR) and (PR=QS) is not sufficient to prove it is a parallelogram. These are properties of an isosceles trapezoid in some cases, so it is not necessarily a parallelogram.

Step5: Analyze fourth figure

In the fourth figure with quadrilateral (STUR), having (ST\parallel UR) and (ST = UR) satisfies the definition of a parallelogram (a quadrilateral with one pair of opposite sides parallel and equal is a parallelogram).

Answer:

First figure: Not necessarily a parallelogram Second figure: Parallelogram Third figure: Not necessarily a parallelogram Fourth figure: Parallelogram