Show that the diagonals of a rectangle have the same length. [Hint: Place the rectangle in...

Show that the diagonals of a rectangle have the same length. [Hint: Place the rectangle in the first quadrant of the plane and label its vertices appropriately, as in Exercises 1–2.]

Exercises 1–2

1. Show that the midpoint M of the hypotenuse of a right triangle is equidistant from the vertices of the triangle. [Hint: Place the triangle in the first quadrant of the plane, with right angle at the origin so that the situation looks like the figure.]

2. Show that the diagonals of a parallelogram bisect each other. [Hint: Place the parallelogram in the first quadrant with a vertex at the origin and one side along the x-axis so that the situation looks like the figure.]