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The most often considered types of bisectors are the segment bisector, a line that passes through the midpoint of a given segment, and the angle bisector, a line that passes through the apex of an angle (that divides it into two equal angles). In three-dimensional space, bisection is usually done by a bisecting plane, also called the bisector.
It can only be used to draw a line segment between two points, or to extend an existing line segment. The compass can have an arbitrarily large radius with no markings on it (unlike certain real-world compasses). Circles and circular arcs can be drawn starting from two given points: the centre and a point on the circle. The compass may or may ...
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose ...
The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC: and conversely, if a point D on the side BC of ABC divides BC in the same ratio as the sides AB and AC, then AD is the angle bisector of angle ∠ A.
The midpoint of any diameter of a circle is the center of the circle. Any line perpendicular to any chord of a circle and passing through its midpoint also passes through the circle's center. The butterfly theorem states that, if M is the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect ...
Isosceles trapezoid. In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of equal measure, [ 1 ...
Let A' be the intersection of IB' and I'B. Then AA' is the angle bisector of ᗉ IAI'. [3] Case 2b: IB' is parallel to I'B Construct the line segment BB' and using a hyperbolic ruler, construct the line OI" such that OI" is perpendicular to BB' and parallel to B'I". Then, line OA is the angle bisector for ᗉ IAI'. [3]
Cevian. In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [1][2] Medians and angle bisectors are special cases of cevians. The name "cevian" comes from the Italian mathematician Giovanni Ceva, who proved a well-known theorem about cevians which also bears his name.