"A figure has opposite sides of equal length" means we have a parallelogram. The same applies to the part about equal slopes (leading to parallel lines)
The diagonals have negative reciprocal slopes, which is another way of saying they are perpendicular. Any time we have perpendicular diagonals, we have a rhombus. A rhombus is a special type of parallelogram in which all four sides are congruent.
This rhombus may or may not have four right angles. So its not clear if this is a square or not. The best we can say is that it's a rhombus.
So the initial statement is false
Answer: False
Note: if we can prove the diagonals are the same length, then we can determine we have a rectangle. If a figure is a rhombus and a rectangle, then it is a square
