How to do this:

Question

649.The midpoints of the sides of a quadrilateral are joined to form a new quadrilateral. For the new quadrilateral to be a rectangle, what must be true of the original quadrilateral?

Answer 1

Diagonals of given rectangle must be orthogonal to each other

Answer 2

Hi Eric J.

A square, when equally divided vertically, gives two identical rectangles. But when cut diagonally, it gives two equal triangles. Both are halves of the same square, but of different shapes.

I’d recommend you draw some squares and rectangles and divide according to the instructions in your problem just to see what they look like.

Answer 3

if the original quadrilateral was a square

then

the inscribed quadrilateral will also be a square