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In Geometry
Only one line can be drawn perpendicular to a given line at a specific point on that line in a plane. This is based on the definition of perpendicular lines, which intersect at a right angle (90 degrees). The uniqueness of this perpendicular line arises from the geometric properties of Euclidean space.
Through two given lines, there can be either zero, one, or infinitely many lines that can be drawn, depending on their relationship. If the two lines are parallel, no line can pass through both. If they intersect, exactly one line can be drawn through their intersection point. If they are coincident (the same line), then infinitely many lines can be drawn through them.
There is exactly one line that can be drawn perpendicular to a given line at a specific point on that line in three-dimensional space. This is because a perpendicular line will intersect the original line at a right angle, and in three-dimensional geometry, any point on a line can have only one such unique perpendicular direction.
intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
In Geometry
Infinity
Only one line can be drawn perpendicular to a given line at a specific point on that line in a plane. This is based on the definition of perpendicular lines, which intersect at a right angle (90 degrees). The uniqueness of this perpendicular line arises from the geometric properties of Euclidean space.
Lines are parallel if they are perpendicular to the same line. Since the lines m and l are parallel (given), and the line l is perpendicular to the line p (given), then the lines m and p are perpendicular (the conclusion).
They are perpendicular lines
One.
Infinite lines because a circle has infinite lines of symmetry.
Parallel
intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
Perpendicular lines passing through a point are at right angles to each other.
Yes, but only in principle. In practice, you won't live long enough. Putting it in more positive terms: No matter how many lines have already been drawn perpendicular to a given line [segment], there's always enough room for a lot more of them.
Any line that is not parallel to the given lines. The transversal that contains the shortest distance between the two parallel lines, is perpendicular to them.