Rectas Perpendiculares, Teoremas y Problemas - Tabla de Contenido

Elementos de Euclides Libro I, 23 Definiciones. 
Ilustración Visual en Una pagina
Rectas Perpendiculares: Definición 10, Libro I.

Puntos, Teoremas y Problemas
Punto de intersección de las rectas perpendiculares.

Mediatriz de un Segmento.
Teoremas y Problemas

Circuncentro del Triangulo Doblando Papel, Video.
Software de Geometría Dinámica "Tabula"
Construcción paso a paso
Construcción de la mediatriz doblando papel.

Rectángulo. Teoremas y Problemas.

Problema de Geometría 823.
Circunferencias Tangentes, Diámetro, Perpendicular, Cuerda, Secante, Triangulo, Área, Punto de Tangencia.

Problema de Geometría 651.
Libro de Lemas de Arquímedes, Proposición 11
Cuerdas Perpendiculares, Cuadrado del Radio.

Problema de Geometría 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular.

Problema de Geometría 649.
Libro de Lemas de Arquímedes, Proposición 10
Tangente, Cuerda, Paralela, Punto medio, Perpendicular.

Problema de Geometría 648.
Libro de Lemas de Arquímedes, Proposición 9
Cuerdas Perpendiculares, Arcos.

Problema de Geometría 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence.

Problema de Geometría 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Problema de Geometría 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.

Problema de Geometría 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius.

Problema de Geometría 629
Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Problema de Geometría 613
Altitude of a Triangle, Perpendicular, Collinear Points.

Problema de Geometría 612
Altitude of a Triangle, Perpendicular, Congruence.

Problema de Geometría 611
Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Problema de Geometría 610
Intersecting Circles, Radius, Parallel, Common Tangent, Angle, 90 Degrees.

Problema de Geometría 609
Triangle, Perpendiculars, 90 Degrees, Collinearity.

Problem 606
Isosceles Triangles, Perpendicular and Rectas Paralelas.

Problema de Geometría 589.
Triangle, Incenter, Incircle, Tangency Points, Midpoint, Perpendicular, Distance.

Problem 578.
Circle, Perpendicular Chords, Midpoints, Curvilinear Triangle, Area, 90 Degrees.

Problema de Geometría 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problema de Geometría 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problema de Geometría 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Problema de Geometría 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.

Problema de Geometría 428.
Quadrant of a circle, Square, Angle bisector, Measurement.

Problema de Geometría 427.
Triangle, Two Altitudes, Square of a Side.

Problema de Geometría 420.
Triangle, Altitude, Angles, Sides, Measurement.

Problema de Geometría 414.
Triangle, Angles, Altitude, Median, Congruence.

Problema de Geometría 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Problema de Geometría 409.
Quadrilateral, Diagonals, Perpendicular, Congruence.

Problema de Geometría 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Problema de Geometría 397.
Triangle, Altitude, Midpoints, Congruence.

Problema de Geometría 396.
Square, Angle Trisectors, Congruence, Area.

Problema de Geometría 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Problema de Geometría 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Problema de Geometría 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Problema de Geometría 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Problema de Geometría 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Problema de Geometría 377.
Triangle, Internal Angle Bisector, Altitude.

Problema de Geometría 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Problema de Geometría 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

Problema de Geometría 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Problema de Geometría 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Problema de Geometría 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Problema de Geometría 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Problema de Geometría 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent.

Problema de Geometría 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

Problema de Geometría 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Problema de Geometría 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Problema de Geometría 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Problema de Geometría 318.
A Scalene triangle, Altitudes, Collinear points.

Problema de Geometría 317.
Right triangle and Inscribed Squares.

Problema de Geometría 316.
Circular segments and Inscribed Squares.

Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square.

Problema de Geometría 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Problema de Geometría 306.
Square, Triangles, Angles, Sides.

Problema de Geometría 305.
Square, Triangles, Angles, Sides.

Problema de Geometría 303.
Triangle, Angle bisector of 90 degrees.

Problema de Geometría 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular.

Problema de Geometría 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular.

Problema de Geometría 293.
Inscribed Quadrilateral, Rectas Perpendiculares, Rectangle, Isosceles Right triangle, Area, Similarity, Rectas Paralelas.

Problema de Geometría 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Rectas Perpendiculares.

Problema de Geometría 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Rectas Perpendiculares.

Problema de Geometría 291.
Triangle, Circle, Circumradius, Rectas Perpendiculares.

Archimedes' Book of Lemmas Proposition 2
Semicircle, tangents, secant line, perpendicular line to diameter. 

Archimedes' Book of Lemmas Proposition 3
Semicircle, perpendicular line to diameter, chords.

Archimedes' Book of Lemmas Proposition 4
Semicircles, perpendicular line to diameter, Arbelos.

Proposition 5
Arbelos, perpendicular line to diameter, Archimedean Twins, Semicircles, Circles

Proposition 9.
Perpendicular chords, sum of arcs.

Proposition 9.
Perpendicular chords, sum of arcs.

Proposition 10
Tangents to a circle, secant line and chords, Parallel.

Proposition 11
 Perpendicular chords  and radius, square.

Proposition 12
Semicircle, Perpendicular to diameter, Chords, Tangents.

Proposition 13
Circle, Diameter, Perpendicular to chords, Congruence.

Proposition 14
Salinon: Semicircles, Perpendicular to diameter, Circles, Areas.

Proposition 15
Circle, Perpendicular to diameter, Inscribed Regular Pentagon, Arc, Midpoint,  Radius.

Euclid's Elements, Book X, Lemma for Proposition 33
One page visual illustration. Perpendicular to a side, Rectas Paralelas.

Problema de Geometría 290.
Internally Tangent circles, Radius, Rectas Perpendiculares, Tangent.

Geometry Expressions.
Rectas Perpendiculares

Problema de Geometría 289: Tangent circles, Radius, Perpendicular, Tangent.

Engineering the Impossible: Chartres Cathedral
Circle, Square, Triangle, Rectas Perpendiculares.

Problema de Geometría 280.
Quadrilateral, Rectas Perpendiculares, , Rectas Paralelas, Area of Squares.

Piet Mondrian, New York City 1941-42 and the Golden Rectangle.
Index.
Rectas Perpendiculares.

Piet Mondrian, Lozenge Composition with Red, Black, Blue, and Yellow 1925,
Pioneer of Geometric abstraction.
Rectas Perpendiculares.

Problema de Geometría 273.
Triangle, Rectas Perpendiculares, Rectas Paralelas, Area of Squares.

Problema de Geometría 252.
Rectangle, isosceles right triangle, Rectas Perpendiculares, square, area.

Problema de Geometría 251.
Parallelogram, sides, diagonals, squares, Rectas Perpendiculares, areas.

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
TracenPoche Interactive Geometry Software
Perpendicular diagonals.

Simson Line. using Tracenpoche Interactive Geometry Software.
Step-by-Step construction, Manipulation, and animation.
Perpendicular diagonals.

Triangle: Incircle, Perpendicular, Angle Bisector.
Using Tracenpoche Interactive Geometry Software.
Step-by-Step construction, Manipulation, and animation
Perpendicular diagonals.

Orthopole of a Triangle
Using TracenPoche Dynamic Geometry Software
Perpendicular diagonals.

Problema de Geometría 237. Quadrilateral, Midpoints, Exterior line, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 236. Quadrilateral, Midpoints, Exterior line, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 235. Parallelogram, Transversal line, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 234. Parallelogram, Line through a vertex, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 233. Parallelogram, Exterior line, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 232. Parallelogram, Line through a vertex, Rectas Perpendiculares.

Problema de Geometría 231. Triangle, Midpoints, Transversal, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 230. Triangle, Midpoints, Transversal, Rectas Perpendiculares.

Problema de Geometría 229. Triangle, Centroid, Transversal, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 228. Triangle, Midpoints, Exterior line, Perpendiculars lines.

Problema de Geometría 227. Triangle, Centroid, Exterior line, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 226. Triangle, Centroid, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 223. Viviani's theorem, Isosceles triangle, Altitude, Distances, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 222. Viviani's theorem, Equilateral triangle, Exterior point, Rectas Perpendiculares, Distances.  

Problema de Geometría 221. Viviani's theorem, Equilateral triangle, Interior point, Distances, Rectas Paralelas.  

Problema de Geometría 219. Rhombus, Rectas Perpendiculares, arithmetic mean, Rectas Paralelas.

Problema de Geometría 218. Right triangle, Altitude and Projections, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 217. Right triangle, Altitude and Projections, Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse, Rectas Perpendiculares.  

Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse, Rectas Perpendiculares.  

Problema de Geometría 205. Right Triangle Area, Exradii relatives to legs or catheti, Rectas Perpendiculares.  

Problema de Geometría 204. Right Triangle, Incircle, Excircles, Inradius, Exradii, Rectas Perpendiculares.  

Problema de Geometría 203. Right Triangle, Excircles, Exradii, Hypotenuse, Rectas Perpendiculares.

Problema de Geometría 202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter, Rectas Perpendiculares.  

Problema de Geometría 201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter, Rectas Perpendiculares.  

Problema de Geometría 200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius, Rectas Perpendiculares.

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation, Rectas Perpendiculares.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation, Rectas Perpendiculares.

Problema de Geometría 179. Rhombus, Square, Diagonal, Angle, Rectas Perpendiculares, Rectas Paralelas.  

Problema de Geometría 137. Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram, Rectas Perpendiculares.  

Problema de Geometría 136. Orthic Triangle, Altitudes, Rectas Perpendiculares, Concyclic Points.  

Problema de Geometría 135. Orthic Triangle, Altitudes, Perpendicular, Rectas Perpendiculares.  

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

Problema de Geometría 112. Area of square and triangle.
Rectas Perpendiculares.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.
Rectas Perpendiculares, Rectas Paralelas.

Triangle and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Rectas Perpendiculares, Rectas Paralelas.

Problema de Geometría 91
Triangulo, Líneas Paralelas, Perpendiculares,
Alturas, Semejanza, Segmentos Proporcionales.

Taylor Circle Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation, Rectas Perpendiculares.
Henry Martyn Taylor and the blind student of mathematics

Problema 78
Circunferencia, Mediatriz, Secante, Punto Medio, Congruencia, Rectas Perpendiculares.

Problema 76
Cuadrado, Circunferencia inscrita, Arco de 90 grados, Lúnula, Áreas curvilíneas, Rectas Perpendiculares.

Interactive Orthopole of a Triangle: Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation, Rectas Perpendiculares.

Problema 70
Triangulo, Altura, Base, Cuadrados Inscritos, Semejanza, Rectas Perpendiculares.

Problema 69
Triangulo, Altura, Base, Cuadrado Inscrito, Semejanza, Rectas Perpendiculares.

Problema 62
Cuadrado, Circunferencia Inscrita, Arco, Diagonal, Rectas Perpendiculares.

Sangaku Geometry Theorem: Cyclic Quadrilateral. Inradii, Rectangle, Rectas Perpendiculares, Rectas Paralelas.

Interactive Hinged tessellation. Square tessellation - Dynamic Geometry.
This Java applet requires Java 1.3 or higher.
Rectas Perpendiculares, Rectas Paralelas.

Triangle and Squares 22
Rectas Perpendiculares, Rectas Paralelas. 

Triangle and Squares 20
Rectas Perpendiculares, Rectas Paralelas.

Problema 49.
Triangulo rectángulo, ceviana, perpendicular.

Triangle and Squares 17, Rectas Perpendiculares.

Problema 39.
Triangulo, Incirculo, Cuadrilátero Inscriptible, Ángulos, Rectas Perpendiculares.

Problema 29.
Triángulo rectángulo, Altura, Bisectriz, Rectas Perpendiculares, Incentro, Circuncentro, Inradio, Diez Conclusiones.

Problema 27.
Triángulo rectángulo, Incentro, Paralelas, Inradios, Rectas Perpendiculares.

Eyeball Theorem: Animated Angle to Geometry Study.
Rectas Perpendiculares, Rectas Paralelas.

Problema 20.
Triángulo rectángulo, Altura, Perpendiculares, Inradios.

Problema 19.
Triángulo rectángulo isósceles, Excentro, Perpendicular y Segmentos, Rectas Perpendiculares.

Parallelogram with Squares theorem Thébault's Theorem.
Rectas Perpendiculares 

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric way of finding the area of a regular dodecagon.