Geometry with isosceles triangles

[Britney2]

2 isosceles triangles ABC and ABD have the same base AB but are in different planes.
Prove that CD is perpendicular to AB.

(It must be proved that CD is perpendicular to one of the planes and then it is perpendicular with every segment of this plane.)
Thanks in advance!

 

[kuruman]

Consider point O, the midpoint of AB. Construct a plane that is perpendicular to AB and contains point O. What special property does this plane have?

 

[HallsofIvy]

Frankly, that seems to me to use a non-standard definition of "perpendicular".

To me the standard definition of perpendicular is "lines p and q are perpendicular if and only if they meet forming right angles." For this two be true we must also allow two skew lines to be perpendicular as long as the projection of one onto a plane containing the other intersects it forming right angles.