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  2. Midpoint theorem (triangle) - Wikipedia

    en.wikipedia.org/wiki/Midpoint_theorem_(triangle)

    The midpoint theorem generalizes to the intercept theorem, where rather than using midpoints, both sides are partitioned in the same ratio. [1] [2] The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle.

  3. Midpoint - Wikipedia

    en.wikipedia.org/wiki/Midpoint

    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 ...

  4. Mixtilinear incircles of a triangle - Wikipedia

    en.wikipedia.org/wiki/Mixtilinear_incircles_of_a...

    Pascal's theorem on hexagon inscribed in implies that ,, are collinear. Since the angles ∠ D A I {\displaystyle \angle {DAI}} and ∠ I A E {\displaystyle \angle {IAE}} are equal, it follows that I {\displaystyle I} is the midpoint of segment D E {\displaystyle DE} .

  5. Isometry - Wikipedia

    en.wikipedia.org/wiki/Isometry

    Definition: [7] The midpoint of two elements x and y in a vector space is the vector ⁠ 1 / 2 ⁠ (x + y). Theorem [ 7 ] [ 8 ] — Let A : X → Y be a surjective isometry between normed spaces that maps 0 to 0 ( Stefan Banach called such maps rotations ) where note that A is not assumed to be a linear isometry.

  6. Midpoint theorem - Wikipedia

    en.wikipedia.org/wiki/Midpoint_theorem

    Midpoint theorem may refer to the following mathematical theorems: Midpoint theorem (triangle) Midpoint theorem (conics) Midpoint theorem, describing the properties ...

  7. Steiner inellipse - Wikipedia

    en.wikipedia.org/wiki/Steiner_inellipse

    According to Marden's theorem, [3] if the three vertices of the triangle are the complex zeros of a cubic polynomial, then the foci of the Steiner inellipse are the zeros of the derivative of the polynomial. The major axis of the Steiner inellipse is the line of best orthogonal fit for the vertices. [6]: Corollary 2.4

  8. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.

  9. Medial triangle - Wikipedia

    en.wikipedia.org/wiki/Medial_triangle

    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.

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