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# Through a given point not on a given line there is exactly one line parallel to the given line?

Updated: 4/28/2022

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Q: Through a given point not on a given line there is exactly one line parallel to the given line?
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Playfair Axiom

### How do you negate the euclidean parallel postulate?

Assume there are no lines through a given point that is parallel to a given line or assume that there are many lines through a given point that are parallel to a given line. There exist a line l and a point P not on l such that either there is no line m parallel to l through P or there are two distinct lines m and n parallel to l through P.

### Which conjecture justifies the construction of a line parallel to a given line through a given point?

Euclid's parallel postulate.

zero

infinitely many

### How many lines are parallel to a line through a point not on the line?

Exactly one. No more and no less.

### What is an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line?

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the given line (-7,3); x=4

### What is eullidean geometry?

"Euclidean" geometry is the familiar "standard" geometry. Until the 19th century, it was simply "geometry". It features infinitely divisible space, up to three dimensions, and, most notably, the "parallel postulate": "Given a line, and a point not on the line, there is exactly one line that can be drawn through the point and parallel to the given line."

### How do you write an equation that is parallel to a given line and passes through the given point?

Parallel straight line equations have the same slope but with different y intercepts

### 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 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