Question

asem is definitely a parallelogram.
a. true
b. false

Explanation:

To determine if ASEM is a parallelogram, we use the property that in a parallelogram, consecutive angles should be supplementary (sum to \(180^\circ\)) if it were a parallelogram with two pairs of parallel sides. However, the given diagram (with angles marked) does not provide enough information to confirm that both pairs of opposite sides are parallel. Just having angles marked doesn't guarantee it's a parallelogram (e.g., it could be a trapezoid or another quadrilateral). But wait, actually, in a parallelogram, opposite angles are equal and consecutive angles are supplementary. But the key here is: the diagram shows a quadrilateral with angles at E, S, M, A. For a quadrilateral to be a parallelogram, both pairs of opposite sides must be parallel (or both pairs of opposite angles equal, or one pair of opposite sides parallel and equal, etc.). The problem states "definitely a parallelogram"—but we can't be sure. Wait, no—actually, the marking of angles (if we assume that the way the angles are marked, but maybe the diagram is a parallelogram? Wait, no, the correct answer: Wait, no, the question is "ASEM is definitely a parallelogram"—the answer is False, because we can't definitively say it's a parallelogram just from the diagram as presented (maybe it's a trapezoid or other quadrilateral). Wait, no, maybe I made a mistake. Wait, in a parallelogram, both pairs of opposite sides are parallel. The diagram shows a quadrilateral with E connected to S, S to A, A to M, M to E? Wait, no, the labels are E, S, A, M: E---S, S---A, A---M, M---E? Wait, no, the order is E, S, A, M: so sides ES, SA, AM, ME. For it to be a parallelogram, ES must be parallel to AM, and SA parallel to ME. The angles: if angle at E and angle at A are equal, angle at S and angle at M are equal (opposite angles), but the problem says "definitely"—but we can't be sure. Wait, no, the correct answer is False because we don't have enough information to say it's definitely a parallelogram. Wait, no, maybe the diagram is a parallelogram, but the key is: the question is whether it's "definitely" a parallelogram. Since we can't be certain (it could be a different quadrilateral), the answer is False.

Answer:

B. False