If two triangles are on a common base and have equal areas, then they will lie between the same parallel lines. Let's draw the given triangle ABC. Since ΔEBC and ΔDBC are lying on a common base BC and they also have equal areas, therefore, ΔEBC and ΔDBC will lie between the same parallel lines. Hence, DE || BC proved.
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If two triangles are on a common base and have equal areas, then they will lie between the same parallel lines. Let's draw the given triangle ABC. Since ΔEBC and ΔDBC are lying on a common base BC and they also have equal areas, therefore, ΔEBC and ΔDBC will lie between the same parallel lines. Hence, DE || BC proved.