To construct a perpendicular segment through a given point using paper folding, start by folding the paper in half to create a crease that represents a line. Then, unfold the paper and fold it such that the given point lies on the crease, ensuring that the crease is perpendicular to the original fold. Finally, the intersection of the two creases will provide the desired perpendicular segment through the point. This method utilizes the properties of folds to achieve precise angles without the need for measurements.
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
By repeating the perpendicular line segment construction twice through paper folding, you can create a square. The first fold establishes a perpendicular line segment, while the second fold can be used to create another perpendicular segment at a right angle to the first, effectively allowing you to define the four corners of a square. This technique leverages the properties of right angles and equal lengths established through the folds.
To achieve this, first, identify the segment and the point not on the segment. Then, fold the paper such that the segment aligns perfectly with its reflection across the folding line that passes through the point. This line should bisect the angle formed by the segment and the perpendicular drawn from the point to the segment, ensuring that the segment overlaps itself when folded. After folding, the segment and its reflection will coincide, demonstrating the desired alignment.
You can construct a parallel to a line through a point not on the line. (perpendicular line segment)
perpendicular line segment (apex)
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
~APEX~ A parallel line through a point not on the line
upon itself
By repeating the perpendicular line segment construction twice through paper folding, you can create a square. The first fold establishes a perpendicular line segment, while the second fold can be used to create another perpendicular segment at a right angle to the first, effectively allowing you to define the four corners of a square. This technique leverages the properties of right angles and equal lengths established through the folds.
You construct a line perpendicular to the original and then a line perpendicular to this second line.
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
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
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