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In Euclidean geometry if there is a line and a point not on the line then there is exactly one line through the point and the parallel to the given line. True or false?
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
What is the shortest path between a line and a point not on that line?
The shortest path is a line perpendicular to the given line that passes through the given point.
What is the shortest segment from any given point to a line is the what segment?
A perpendicular to the line which passes through the given point.
Writing an equation given a slope and a point?
If the slope m is given at a point (xo, yo) of a line, then the equation of the line is given by: y - yo = m(x - xo)
Only 1 line can be drawn perpendicular to a given line at a given point?
Yes (in a Euclidean plane)..
What is needed to determine a line?
Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.
Constructions can be accomplished with paper folding?
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line
What constructions can be accomplished with paper folding?
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line
What constructions can be accomplishments with paper-folding?
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line
What constructions can be accomplished paper folding?
Finding the midpoint of a segment Drawing a perpendicular line segment from a given point to a given segment Drawing a perpendicular line segment through a given point on a given segment Drawing a line through a given point parallel to a given line
What is the shortest path between a line and a point not on that line?
The shortest path is a line perpendicular to the given line that passes through the given point.
What is the shortest segment from any given point to a line is the what segment?
A perpendicular to the line which passes through the given point.
What is the shortest segment from a point to line?
A line that is perpendicular to the given line and passes through the given point.
What does a given point repesent on a line graph?
A given point of x and y
Through a given point on a given line there is exactly one line parallel to the given line what does it define?
Playfair Axiom
Through a given point not on a given line there is exactly one line parallel to the given line?
The Playfair Axiom (or "Parallel Postulate")
To construct a line perpendicular to a given line through a point fold the paper through the point so that the given line segment lies?
upon itself
