Exercise 31 Page 533

Let's analyze the given quadrilateral to find the length EG. Keep in mind that we have been told that the quadrilateral is a rectangle.

By the Segment Addition Postulate, we can express each diagonal as the sum of its smaller segments. Therefore, FH is the addition of FK and KH. FH= FK + KH Additionally, because a rectangle is a parallelogram, we know that the diagonals bisect each other. This means that FK and KH have the same length. FK=KH Let's use this information to find the length of FH. Recall that we know that FK=32.

Now, recall that the diagonals of a rectangle are congruent. Therefore, their lengths are equal. FH = EG ⇔ EG = 64