Fold the paper so the line is on itself.
Fold this folded edge on itself causing a crease to form that goes through the point in question,
You are using the theorem that lines perpendicular to the same line are parallel.
true
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the 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
To find the midpoint of a line segment using paper folding constructions, first fold the paper so that the two endpoints of the line segment coincide. Then, make a crease along the folded line. Unfold the paper and the crease will intersect the line segment at its midpoint. This method utilizes the properties of parallel lines and corresponding angles to accurately locate the midpoint of the line segment.
To find a segment parallel to another segment through a given point using paper folding techniques, first, fold the paper so that the given point aligns with one endpoint of the original segment. Next, fold the paper again to create a crease that intersects the original segment, ensuring that the distance between the two segments remains constant, thus establishing a parallel segment through the given point.
true
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
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
Yes, you can find the midpoint of a segment using folding constructions. By folding the segment so that its endpoints coincide, the crease created by the fold will represent the midpoint of the segment. This method relies on the properties of symmetry and congruence inherent in folding. Thus, it is a valid geometric construction technique.