Question

Сформулировать теорему о трёх перпендикулярах

Answer 1

Если прямая, лежащая в плоскости, перпендикулярна проекции наклонной на эту плоскость, то она перпендикулярна и самой наклонной.
и обратная:
если прямая, лежащая в плоскости, перпендикулярна наклонной, то она перпендикулярна и самой проекции на эту плоскость.

Answer 2

Theorem of Three Perpendiculars

The theorem of three perpendiculars states that in a triangle, the following three perpendiculars intersect at one point:

1. The perpendicular from any vertex to the opposite side. 2. The perpendicular from any vertex to the line containing the opposite side. 3. The perpendicular from the orthocenter to any side of the triangle.

This theorem is fundamental in the study of triangles and their properties. It provides a key insight into the relationships between the various elements of a triangle and the concept of perpendicularity within the context of triangle geometry.

The theorem of three perpendiculars is a significant result in Euclidean geometry and is widely used in various geometric proofs and constructions.