In triangle ABC, the sum of the angles A and B is 90 °. line BD is perpendicular to plane ABC.

In triangle ABC, the sum of the angles A and B is 90 °. line BD is perpendicular to plane ABC. Prove that CD is perpendicular to AC.

The ABC triangle is rectangular, the angle C is 90 °, since 180 ° – (A + B) = 180 – 90 = 90 °.

This means that the BC is perpendicular to the AC.

VD is perpendicular to the plane ABC, therefore, ВD is perpendicular to the AС

On the basis of the perpendicularity of a straight line and a plane, the AC is perpendicular to the ВDС plane, since it is perpendicular to two straight lines in this plane.

Consequently, the AС is perpendicular to the DС.