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They are just different names for the same shape.

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Actually, they are not. A rhombus is a parallelogram with all its sides of the same length. It is, therefore a special kind of parallelogram. (Just like a square is a special kind of rectangle). So all properties of a parallelogram apply to a rhombus.

Q: What are the similarities of a rhombus and a parallelogram?

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A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.

A rhombus is a parallelogram, but something that is a parallelogram isn't necessarily a rhombus.

a parallelogram will never ever be a rhombus

A rhombus is always a parallelogram, by definition.

A rhombus is always a parallelogram!

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A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.

A rhombus is a parallelogram, but something that is a parallelogram isn't necessarily a rhombus.

A rhombus is a parallelogram.

a parallelogram will never ever be a rhombus

An equilateral parallelogram is a rhombus.

A rhombus is always a parallelogram!

A rhombus is always a parallelogram, by definition.

No. A rhombus is a type of parallelogram.

A square is a special case of a rhombus. A parallelogram is not 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.

Yes, that's a true statement.A rhombus is a special case of a parallelogram.

A rhombus is a special kind of parallelogram: one in which all sides are equal. It is not true to say that a parallelogram is never a rhombus.