Teoremas y Problemas de Geometria, Pre-Universitaria, Bachillerato

Geometría Plana: Punto Medio, Teoremas y Problemas - Tabla de Contenido

Ounto medio, Teoremas y Problemas Indice 

El Punto, Teoremas y Problemas, Indice

Puntos, Teoremas y Problemas

Mediatriz, Teoremas y Problemas

Mediatriz de un Segmento.
Punto medio, Teoremas y Problemas

Teorema de la Mariposa Demostración animada.
Punto medio de una cuerda.

Trapezoid median, Theorems and Problems, Index

Mediana del Trapecio, Teoremas y Problemas .

Teorema de Newton: Recta de Newton. Cuadrilátero circunscrito, Puntos medios de las diagonales, Centro de la circunferencia inscrita.

Cuadrilátero Equílico.
60, 120 grados. Puntos medios
. 

Teorema de Kurschak. Jozsef Kurschak (Hungría, 1864-1933) Elegante forma de encontrar el área de un dodecágono regular a partir de los puntos medios de los lados de un cuadrado.

Paralelogramos de Varignon y Wittenbauer. Cuadrilátero: Puntos medios y trisección de los lados.

 

Median Length theorem

Longitud de la Mediana, Teorema de Apolonio
Puntos medios.

Van Aubel

Teorema de van Aubel. Cuadrilátero con cuadrados sobre sus lados. Demostración animada.
Puntos medios. 

Punto Simediano (Lemoine)
Puntos notables del triangulo

Archimedes' Book of Lemmas: Proposition 7
Square and inscribed and circumscribed Circles
Puntos medios.

Archimedes' Book of Lemmas: Proposition 2
Semicircle, diameter, tangents, secant line. 
Puntos medio.

Archimedes' Book of Lemmas: Proposition 3
Semicircle, perpendicular to diameter, chords.
Puntos medio.

Archimedes' Book of Lemmas: Proposition 10
Tangents to a circle, secant line and chords, Parallel.
Puntos medio.

Archimedes' Book of Lemmas: Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Puntos medio, Perpendicular, Radius
.

Bottema Theorem. Elearning.

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Puntos medios.

Eight Point Circle Theorem. Elearning

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
Perpendiculars from the Puntos medios.

Marion Walter's Theorem: Triangle and Hexagon areas: Using TracenPoche Dynamic Geometry Software.
Puntos medios.

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.

Mascheroni Construction with compass alone. Puntos medio of a segment.

Heron's Formula with medians.
Puntos medios.

Mittenpunkt Point
Puntos medios. 

Scalene Triangle, Median, Perpendicular, Angle, Measurement

Geometry Problem 802
Scalene Triangle, Median, Perpendicular, Angle, Measurement.

Equilateral Triangles, Midpoint

Geometry Problem 801
Equilateral Triangles, Cevian, Puntos medio, Distance, Measurement, Metric Relations.

Right Triangle, Altitude, Incircles, CIrcumcircles, COngruence

Geometry Problem 795
Intersecting Circles, Common Chord, Puntos medio, Tangent, Secant Line, Perpendicular, 90 Degrees.

Regular Hexagon, Midpoints, Equilateral Triangle

Geometry Problem 791
Regular Hexagon, Puntos medios of Side and Diagonal, Equilateral Triangle, Area.

Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral

Geometry Problem 788
Intersecting Circles, Secant Line, Puntos medio, Cyclic Quadrilateral.

Triangle, Orthocenter, Midpoint

Geometry Problem 784
Triangle, Orthocenter, Puntos medio of a side, Perpendicular.

Triangle, Orthocenter, Circumcircle, Diameter, Midpoint

Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Puntos medio.

Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular

Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Puntos medio, Perpendicular.

Triangle, Orthocenter, Midpoint, 90 Degrees

Geometry Problem 779
Triangle, Altitude, Orthocenter, Puntos medio, Angle, 90 Degrees.

Triangle, Isogonal lines, Congruent angles, Perpendicular

Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center, Puntos medio.

Intersecting Circles, Midpoint, Secant, Bisection

Geometry Problem 773
Intersecting Circles, Puntos medio, Secant line, Bisection.

Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations

Geometry Problem 772
Similar triangles with a Common Vertex, Equal Angles, Puntos medios, Metric relations.

Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence

Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Puntos medio of arc, Parallel to chord, Congruence.

Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle

Geometry Problem 762
Parallelogram, Puntos medio, Perpendicular, Congruence, Isosceles triangle.

Equilateral triangle, Circumcircle, Midpoint

Geometry Problem 755.
Equilateral Triangle, Circumcircle, Chord, Arc, Puntos medios, Perpendicular.

Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Midpoint

Geometry Problem 742.
Scalene Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Puntos medio, Distance, Square, Metric Relations.

Triangle, Incenter, Circumcircle

Geometry Problem 741.
Scalene Triangle, Incenter, Circumcircle, Puntos medio, Arc, Congruence.

Triangle, Median, Isosceles, Congruence, Parallel

Geometry Problem 734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence, Puntos medio.

Triangle, Orthocenter, Circumcircle

Geometry Problem 729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Puntos medio.

Isosceles Triangle, Perpendicular, Midpoint

Geometry Problem 726.
Isosceles Triangle, Perpendicular, Puntos medio, 90 Degrees.

Kurschak Dodecagon

Geometry Problem 725.
Kurschak's Dodecagon, Square, Equilateral Triangle, Puntos medios, 30, 60 Degrees.

Triangle, Parallel, Concurrent, Ceva, Midpoint

Geometry Problem 714.
Triangle, Parallel, Cevians, Puntos medios, Median, Ceva Theorem.

Rectangle, Midpoint, Concyclic points

Geometry Problem 711.
Rectangle, Puntos medio, Angle, Concyclic Points, Cyclic Quadrilateral.

Parallelogram, Midpoint, Diagonal, Collinear, Metric Relations, Similarity, Congruence

Geometry Problem 710.
Parallelogram, Puntos medio, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence.

Parallelogram, Midpoints, Diagonal

Geometry Problem 709.
Parallelogram, Puntos medio, Diagonal, Metric Relations, Triangle.

Orthocenter, triangle, midpoint, perpendicular

Geometry Problem 704.
Triangle, Orthocenter, Altitude, Puntos medio, Perpendicular.

Triangle, Circle, Median, Proportion

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Parallelogram, Midpoint, Diagonal

Geometry Problem 677.
Parallelogram, Puntos medio, Diagonal, Metric Relations.

Triangle, Circumcircle, Incenter

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Puntos medio, Collinear points, Mind Map.

Triangle, Angle Bisectors, Midpoint, Collinear

Geometry Problem 632.
Triangle, Interior and Exterior Angle Bisectors, Puntos medios, Collinear Points.

Triangle, Incircle, Altitude, Incenter, Angle

Geometry Problem 594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Puntos medio, Altitude, Angle, Half the Difference.

Triangle, Incircle, Inradius, Midpoint, Concurrency

Geometry Problem 592.
Triangle, Incenter, Incircle, Tangency Point, Puntos medios, Concurrent Lines, Congruence.

Triangle, Incircle, Inradius, Altitude, Midpoint

Geometry Problem 591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Puntos medio, Altitude.

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