Prove the angle is right

neutrino69

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Apr 21, 2020
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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)!

Problem.jpg
 
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)!

View attachment 18092
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