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To construct a parallel to a line through a point not on the line using paper folding you can perform the ----- construction twice?
perpendicular line segment (apex)
What can you construct if you repeat the perpendicular line segment construction twice using paper folding?
~APEX~ A parallel line through a point not on the line
If you repeat the perpendicular line segment construction twice using paper folding what can you construct?
~APEX~ A parallel line through a point not on the line
Which is not a step when constructing a line parallel to the x-axis of a coordinate plane through a point?
One step that is not involved in constructing a line parallel to the x-axis through a given point is determining the slope of the line to be constructed. A line parallel to the x-axis has a constant y-coordinate, so the only requirement is to maintain the same y-value as the given point while varying the x-coordinate. Thus, the construction simply involves drawing a horizontal line through the specified point.
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.
Which conjecture justifies the construction of a line parallel to a given line through a given point?
Euclid's parallel postulate.
To construct a parallel to a line through a point not on the line using folding you can perform the construction twice?
perpendicular line segment (apex)
To construct a parallel to a line through a point not on the line using paper folding you can perform the ----- construction twice?
perpendicular line segment (apex)
If you repeat the perpendicular line segment construction twice using paper folding what can you construct?
~APEX~ A parallel line through a point not on the line
What can you construct if you repeat the perpendicular line segment construction twice using paper folding?
~APEX~ A parallel line through a point not on the line
If you repeat the perpendicular line segment construction twice using paper folding, you can construct?
~APEX~ A parallel line through a point not on the line
What if you repeat the perpendicular line segment construction twice using paper folding you can construct?
You can construct a parallel to a line through a point not on the line. (perpendicular line segment)
Which is not a step when constructing a line parallel to the x-axis of a coordinate plane through a point?
One step that is not involved in constructing a line parallel to the x-axis through a given point is determining the slope of the line to be constructed. A line parallel to the x-axis has a constant y-coordinate, so the only requirement is to maintain the same y-value as the given point while varying the x-coordinate. Thus, the construction simply involves drawing a horizontal line through the specified point.
To construct a parallel to a line through a point not on the line using paper folding you can perform the construction twice?
perpendicular line segment (apex)
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.
When you construct a parallel to a line through a point not on the line using paper folding what construction can you perform twice?
You construct a line perpendicular to the original and then a line perpendicular to this second line.
What construction do you perform twice when you are constructing a parallel to a line through a point not on the line using paper folding?
You construct a line perpendicular to the original and then a line perpendicular to this second line.
