Q: What must mean almost the opposite of narrow?

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Yes, they must be.

I suppose you mean what is an opposite reciprocal? At any rate, we should start there. The opposite reciprocal is -(1/x) so let's take the number 5. The opposite reciprocal would be -1/5. If you want two lines to be perpendicular you must take the original slope of the first line and change it to its opposite reciprocal. For example: y=5x A line perpendicular to this line would be y=-1/5x.

For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent.

You cannot circumscribe a "true rhombus". The opposite angles of a circumscribed quadrilateral must be supplementary whereas the opposite angles of a rhombus must be equal. That means a circumscribed rhombus is really a square.

I believe they do need to because it stays balanced.

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