Hello, Joanne!

Prove that the figure formed by connecting the adjacent midpoints of any rectangle is a rhombus.

First, make a sketch . . . Code:

P
A * - - - - - * - - - - - * B
| * * |
| * * |
| * * |
S * * Q
| * * |
| * * |
| * * |
D * - - - - - * - - - - - * C
R

Let be the rectangle and be the midpoints.

There are right triangles in each corner.

We can prove that they are all congruent.

Therefore: . . and is a rhombus.

For example, consider and

. . . Opposite sides of a rectangle are equal.

is the midpoint of ; is the midpont of

. .

is the midpont of

Hence: .

Therefore: .

Continue in the same manner and prove all the hypotenuses are equal.