Question 1017250
the slope of a horizontal line is 0.
the slope of a vertical line is undefined.


the rule that the lines are perpendicular to each other when the product of the slopes is equal to -1 only works when both slopes are defined.


in the case of a horizontal line and a vertical line, that rule can't be used.


the rule that can still be used is that the slope of a line perpendicular to another line must be a negative reciprocal of the slope of that line.


the slope of the horizontal line is 0.


the negative reciprocal of 0 is -1 / 0 which is undefined.


since the slope of the vertical line is undefined, it must be perpendicular to the horizontal line.


here's a proof that the parallelogram is a rhombus if the diagonals are perpendicular.


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they did not say, however, that the figure in the graph was a parallelogram.


the proof depends on the figure being a parallelogram.


you are just shown the graph.


the properties of a rhombus are:


the diagonals are perpendicular.
the figure is a parallelogram.


to show the figure is a parallelogram, you have to show that the opposite sides are parallel and are congruent.


once you've shown that, you can then say that it must be a rhombus because, on top of that, the diagonals are perpendicular.


but, if you showed the opposite sides are parallel and that all the sides are congruent, then you've satisfied the definition of a rhombus.


also, in a parallelogram, the diagonals bisect each other.


that is not necessarily true in a quadrilateral, unless the quadrilateral is a parallelogram.


so, besides the fact that you struggled with the diagonals being perpendicular to each other, i think you have to show that the opposite sides are parallel (use their slopes), and that the opposite sides are congruent.


that says it's a parallelogram.


then, either all 4 sides are congruent to each other, which you would probably find after you measured all their lengths.


once you've done that, you don't need to state that the diagonals are perpendicular, although that would be icing on the cake.


before you can prove it's a rhombus, you have to prove it's a parallelogram, because a rhombus is a special kind of parallelogram.


here's a definition of a rhombus from wikipedia at <a href = "https://en.wikipedia.org/wiki/Rhombus" target = "_blank">https://en.wikipedia.org/wiki/Rhombus</a>


A simple (non self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:[6][7]


    a quadrilateral with four sides of equal length (by definition)
    a quadrilateral in which the diagonals are perpendicular and bisect each other
    a quadrilateral in which each diagonal bisects two opposite interior angles
    a parallelogram in which a diagonal bisects an interior angle
    a parallelogram in which at least two consecutive sides are equal in length
    a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram)


any one of these definition defines a rhombus.