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An equilateral parallelogram is a rhombus.
If the sides of a parallelogram are all of the same length then it is a rhombus. Thus, a rhombus is a special type of parallelogram.
Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.
Every rhombus is a parallelogram.
False.Every parallelogram is not a rhombus, but every rhombus is also a parallelogram.