We are given a square WXYZ and the point of intersection of the diagonals T. We also know that the length of the segment WT is 3.
Let's begin by recalling that a square is a special type of parallelogram. This means all of properties of parallelograms apply to squares. We know that the diagonals of a parallelogram bisect each other. Using this property, we can say that the lengths of segments WT and TY are equal.
TY = WT ⇔ TY = 3
Next, using the Segment Addition Postulate, we can evaluate the length of the diagonal YW. To do so, we will write YW as a sum of TY and WT.
We have found the length of the segment YW. Next, recall that a square is also a rectangle. This means that our square also has congruent diagonals. Therefore, the segment ZX has the same length as the segment YW.
ZX = YW ⇔ ZX = 6
We found that the diagonal ZX of the given square WXYZ has a length of 6.
