Question

In parallelogram ABCD, where AB = m and BC = n, point C is the midpoint of line BD. Find the value of FD in terms of m and n.

Answer 1

To find FD, observe that in parallelogram ABCD with AB = m and BC = n, since C is the midpoint of BD, FD must be half of BD. Because BD consists of two lengths of BC, FD = BC = n.

Step-by-step explanation:

The question involves finding the length of line segment FD in a parallelogram ABCD, given that AB = m, BC = n, and C is the midpoint of BD. Since ABCD is a parallelogram, opposite sides are equal, meaning AD = BC = n and AB = CD = m. Now, since C is the midpoint of BD, BC would be equal to CD, which means BD is twice the length of BC, thus BD = 2n. To find FD, we need to consider triangle BFD. Since C is the midpoint of BD, BC = CD, which means CF = FD and is half of BD. So, FD = BD / 2 = 2n / 2 = n. Therefore, FD is of length n.