What does bisector mean in math?
What does bisector mean in math?
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. In three-dimensional space, bisection is usually done by a plane, also called the bisector or bisecting plane.
What do you mean by the term bisect?
transitive verb. : to divide into two usually equal parts.
What is a bisector of a line?
To bisect a segment or an angle means to divide it into two congruent parts. A bisector of a line segment will pass through the midpoint of the line segment. A perpendicular bisector of a segment passes through the midpoint of the line segment and is perpendicular to the line segment.
What is the bisector of a triangle?
An angle bisector of a triangle is a segment, ray or line which divides an angle of the triangle into two congruent (equal in measure) parts. Since all triangles have three angles, all triangles have three angle bisectors.
How do you find the length of a bisector in a triangle?
The length of the angle bisector of a standard triangle such as AD in figure 1.1 is AD2 = AB · AC − BD · DC, or AD2 = bc [1 − (a2/(b + c)2)] according to the standard notation of a triangle as it was initially proved by an extension of the angle bisector up to the circumcircle of the triangle.
What is equidistant from the three vertices of the triangle?
The CIRCUMCENTER of a triangle is the point in the plane equidistant from the three vertices of the triangle.
How do you solve an equidistant problem?
Step 1: Find the distance between the points A(x, 6) and C(6, -4). Step 2: Find the distance between the points A(x, 6) and D(14, 8). Step 3: AC = AD, since AC and AD are equidistant.
How do you prove a point is equidistant?
If the point is on the perpendicular bisector of a segment, then it’s equidistant from the endpoints of the segment. (Here’s an abbreviated version: If you have a perpendicular bisector, then there’s one pair of congruent segments.)
Why is a Circumcenter special?
One of a triangle’s points of concurrency. One of several centers the triangle can have, the circumcenter is the point where the perpendicular bisectors of a triangle intersect. The circumcenter is also the center of the triangle’s circumcircle – the circle that passes through all three of the triangle’s vertices.