perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
perpendicular line segment (apex)
You construct a line perpendicular to the original and then a line perpendicular to this second line.
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.
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
A conjecture
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
You can construct a parallel to a line through a point not on the line. (perpendicular line segment)
To construct a parallel line through a point not on the line using paper folding, you can perform the "folding to find the perpendicular" construction twice. First, fold the paper so that the point aligns with the line, creating a crease that indicates the perpendicular. Then, unfold and fold again using the newly created crease as a reference to establish a line parallel to the original through the given point. This method ensures that the resulting line is parallel to the original line.
perpendicular line segment (apex)
You construct a line perpendicular to the original and then a line perpendicular to this second line.
You construct a line perpendicular to the original and then a line perpendicular to this second line.