In parallelogram ABCD, P is a point outside ad, and AP is vertical to PC, BP is vertical to PD, so find parallelogram ABCD as rectangle

It is proved that connecting AC and BD intersects at point o
Connect op
A quadrilateral ABCD is a parallelogram
∴AO=OC,BO=OD
∵∠APC=90°
Ψ OP = 1 / 2Ac (the middle line of the hypotenuse of a right triangle equals half of the hypotenuse)
The same is true
OP=1/2BD
∴AC=BD
A quadrilateral ABCD is a parallelogram (a parallelogram with equal diagonals is a rectangle)

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