Prove the angle is right

[neutrino69]

Let D be an arbitrary point on the hypotenuse AB of right angled triangle ABC.
The line drawn from C and perpendicular to the hypotenuse (green) and line drawn through point D parallel with side AC (blue) give the intersection point E.
Prove that line CD (red) is perpendicular to line BE (magenta)!

 

[Deleted member 4993]

Let D be an arbitrary point on the hypotenuse AB of right angled triangle ABC.
The line drawn from C and perpendicular to the hypotenuse (green) and line drawn through point D parallel with side AC (blue) give the intersection point E.
Prove that line CD (red) is perpendicular to line BE (magenta)!

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