Question

In a rectangle ABCD, P is any interior point then prove that PA² +PC²=PB²+PD²

Answer 1

Answer:

draw a rectangle and label the corners ABCD.

Pick any point in the interior, label it P.

Join P to all 4 corners by drawing lines and also draw the vertical lines (parallel to the 2 vertical sides) from P to the base and top of the rectangle.

Now you can use Pythagoras' theorem on the 4 resulting right-angled triangles.