The perpendicular line segment construction involves creating a line segment that meets another line at a right angle (90 degrees). This is typically done using a compass and straightedge. First, a point is marked on the line where the perpendicular will intersect. Then, arcs are drawn from this point to establish two points equidistant from it, allowing the straightedge to connect these points, forming a perpendicular line.
equilateral triangles
perpendicular bisector
If you repeat the perpendicular line segment construction twice, you would create a series of perpendicular lines that relate to the original segment. The first construction establishes a perpendicular line at a specific point, and the second construction can either create another perpendicular line from a new point on the first line or extend the process further. This process effectively builds a geometric framework that can be used to explore relationships between angles and distances in the plane. Ultimately, you would have multiple lines that maintain perpendicular relationships, enhancing the geometric complexity of your figure.
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line
You can construct a parallel to a line through a point not on the line. (perpendicular line segment)
Equilateral triangles
equilateral triangles
perpendicular bisector
It's called a perpendicular bisector of the line segment.
perpendicular line segment (apex)
Perpendicular Bisector
If you repeat the perpendicular line segment construction twice, you would create a series of perpendicular lines that relate to the original segment. The first construction establishes a perpendicular line at a specific point, and the second construction can either create another perpendicular line from a new point on the first line or extend the process further. This process effectively builds a geometric framework that can be used to explore relationships between angles and distances in the plane. Ultimately, you would have multiple lines that maintain perpendicular relationships, enhancing the geometric complexity of your figure.
A property used in the construction of a perpendicular bisector is that it divides a line segment into two equal parts while forming right angles (90 degrees) with the segment. This means that any point on the perpendicular bisector is equidistant from the segment's endpoints.
The perpendicular bisector of a line segment AB is the straight line perpendicular to AB through the midpoint of AB.
perpendicular line segment (apex)
~APEX~ A parallel line through a point not on the line