What does the term bisectmean?
The term “bisect” is important in geometry; it means to cut into two (or divide into half)
mainly lines (or two-dimensional figures) and angles. To compare, a bisected line seg-
ment means finding the plane, line, or point that is the midpoint of the line segment.
This is also called a segment bisector. An angle bisector is a ray in the interior of an
angle that forms two equal angles. First locate the point on each ray that is equally dis-
tant from the vertex; then draw a third point equally distant from each of the first two
rays. A line that extends through the third point and the vertex is the angle bisector.
To draw a bisector, follow this sequence (as per the illustration above): First, draw
an angle; then draw an arc centered at the vertex (endpoint), in which B and C are the
intersections of the arc and angle lines at equal distances from the vertex; next draw
an arc centered at B and one centered at C—both with the same radii—inside the
angle; finally, extend a line from the vertex to the point D where the arcs of B and C
intersect—making AD the bisector of the angle at A.
What are geometric postulates?
Similar to other parts of mathematics, there are many geometric postulates, or
statements that are assumed to be true without proof. From these postulates, theo- 177
GEOMETRY AND TRIGONOMETRY
Examples of a perpendicular line (top), normal lines
(middle), and tangential lines (bottom), with point
M being the point of tangency.
To determine a bisector, follow these steps from top to
bottom: Draw an angle; draw an arc from the angle’s
vertex that touches the two angle lines; draw two
more arcs from the points where the first arc meets
the angle lines; draw a line from point A to point D.