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The midpoint theorem, midsegment theorem, or midline theorem states that if the midpoints of two sides of a triangle are connected, then the resulting line segment will be parallel to the third side and have half of its length.
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
The red triangle is the medial triangle of the black. The endpoints of the red triangle coincide with the midpoints of the black triangle. In Euclidean geometry, the medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC, BC.
The 'interior' or 'internal bisector' of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The 'exterior' or 'external bisector' is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of ...
The following formula relates the radius of the incircle and the radius of the -mixtilinear incircle of a triangle : = where α {\displaystyle \alpha } is the magnitude of the angle at A {\displaystyle A} .
The angle bisector theorem is commonly used when the angle bisectors and side lengths are known. It can be used in a calculation or in a proof. An immediate consequence of the theorem is that the angle bisector of the vertex angle of an isosceles triangle will also bisect the opposite side.
The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle. In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.
To draw only a certain arc from an angle to an angle , the algorithm needs first to calculate the and coordinates of these end points, where it is necessary to resort to trigonometric or square root computations (see Methods of computing square roots). Then the Bresenham algorithm is run over the complete octant or circle and sets the pixels ...