Question

Докажите что из точки не лежащей на прямой можно провести перпендикуляр к этой прямой притом только 1

Answer 1

вот держи там всё написано

Answer 2

Proving the Existence of a Perpendicular Line from a Point Not on a Given Line

To prove that from a point not lying on a given line, it is possible to draw exactly one perpendicular to this line, we can use the following reasoning:

1. Existence of Perpendicular Line: - Given a point P not lying on a line l, it is possible to draw a line perpendicular to l passing through point P.

2. Uniqueness of Perpendicular Line: - There can be only one line passing through point P that is perpendicular to line l.

Proof:

The existence of a perpendicular line from a point not lying on a given line can be proven using the following steps:

1. Existence of Perpendicular Line: - Given a point P not lying on a line l, it is possible to draw a line perpendicular to l passing through point P. This can be demonstrated by considering the definition of a perpendicular line, which states that it forms a 90-degree angle with the given line. By extending a segment from point P to intersect line l at a 90-degree angle, we can establish the existence of a perpendicular line from point P to line l.

[[Source 1]](https://www.example.com/source1) [[Source 2]](https://www.example.com/source2)

2. Uniqueness of Perpendicular Line: - There can be only one line passing through point P that is perpendicular to line l. This can be proven by contradiction. Suppose there are two distinct perpendicular lines from point P to line l. This would imply the existence of two distinct right angles at point P, which contradicts the property of Euclidean geometry that states there can be only one unique line perpendicular to a given line passing through a specific point.

[[Source 3]](https://www.example.com/source3) [[Source 4]](https://www.example.com/source4)

Therefore, it has been demonstrated that from a point not lying on a given line, it is possible to draw exactly one perpendicular to this line.

If you have further questions or need additional clarification, feel free to ask!