The diagonals of a square are always perpendicular.
Proof: Without loss of generality, assume the square has side length 1 and one vertex is at the origin. The square ABCD is given by:
A = (0,0) , B = (1,0) , C = (1,1) , D = (0,1)
The diagonals are d1=AC and d2=BD. Finding equations for each of them yields
d1 = x
d2 = 1-x (you can double check this)
So, the relative slopes are 1 and -1. Since their product is -1, they are perpendicular.
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No but the diagonals of a square, rhombus and a kite are perpendicular to each other
No.
Two.
none, no
Not always but they are perpendicular in a square, a rhombus and a kite in that the diagonals intersect each other at 90 degrees