Midpoint, Theorems and Problems - Table of Content

Points, Theorems and Problems - Index.

Butterfly Theorem Proof with animation.
Midpoint of a chord.

Median of a Trapezoid, Theorems and Problems. Index.

Newton's Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of diagonals, center of the circle inscribed.

Equilic Quadrilateral.
120 degrees. Midpoints. 

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.
Midpoints. 

Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and trisection points of the edges.

Median length, Apollonius' Theorem
Midpoints.

Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.
Midpoints. 

Symmedian (Lemoine) Point
Triangle Center

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

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

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

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

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

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

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

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

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

Mascheroni Construction with compass alone. Midpoint of a segment.

Heron's Formula with medians.
Midpoints.

Mittenpunkt Point
Midpoints. 

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.
Midpoints.

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs. Midpoints.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area. Midpoints.

Newton's Theorem, Newton-Gauss Line: Complete quadrilateral theorem. Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation. Midpoints.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

Proposed Problem 321.
Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity.

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

Proposed Problem 308.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 286: Square, Midpoints, Octagon.

Proposed Problem 276.
Square, 90 degree Arcs, Circle, Radius.
Midpoints.

Proposed Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius.
Midpoints.

Sagitta, Arc, Chord.
Midpoints.

Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.
Midpoints.

Centroid /Barycenter. Index.
Medians, Midpoints.

Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Midpoints.

Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Midpoints.

Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.
Midpoints.

Proposed Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.

Proposed Problem 244. Square, Diagonals, Centers, Distance.
Midpoints.

Proposed Problem 239. Square, Midpoints, Lines, Congruence, Pythagoras.

Proposed Problem 238. Square, Midpoints, Lines, Congruence.

Proposed Problem 237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Proposed Problem 236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Proposed Problem 231. Triangle, Midpoints, Transversal, Perpendicular lines.

Proposed Problem 230. Triangle, Midpoints, Transversal, Perpendicular lines.

Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular lines.
Midpoints.

Proposed Problem 228. Triangle, Midpoints, Exterior line, Perpendiculars lines.

Proposed Problem 227. Triangle, Centroid, Exterior line, Perpendicular lines.
Midpoints.

Proposed Problem 226. Triangle, Centroid, Perpendicular lines.
Midpoints.

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.
Midpoints.

Proposed Problem 218. Right triangle, Altitude and Projections.
Midpoints.

Proposed Problem 217. Right triangle, Altitude and Projections.
Midpoints.

Proposed Problem 183. Right Triangle, Hypotenuse Trisection Points, Squares of the Distances.
Midpoints.

Proposed Problem 178. Quadrilateral, Trisection of sides, Area.
Midpoints.

Proposed Problem 177. Parallelogram with Midpoints, Triangles, Areas.  

Proposed Problem 176. Quadrilateral with Midpoints, Triangles, Areas.  

Proposed Problem 175. Quadrilateral with Midpoints, Areas.  

Proposed Problem 174. Quadrilateral with Midpoints, Triangles, Areas.  

Proposed Problem 173. Quadrilateral with Midpoints, Triangles, Areas.  

Proposed Problem 172. Trapezoid, Midpoints, Quadrilaterals, Areas.  

Proposed Problem 171. Trapezoid, Midpoints, Triangles, Areas.  

Proposed Problem 170. Trapezoid, Midpoint, Triangle, Area.  

Proposed Problem 161. Parallelogram, Midpoints, Octagon, Areas.  

Proposed Problem 151. Quadrilateral, Area, Trisection of Sides.
Midpoints.

Proposed Problem 150. Quadrilateral, Area, Trisection of Sides.
Midpoints.

Proposed Problem 149. Quadrilateral, Area, Midpoints.

Proposed Problem 148. Quadrilateral, Area, Midpoints.

Proposed Problem 147. Quadrilateral, Area, Midpoints, Triangle.

Proposed Problem 146. Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Proposed Problem 132.
Triangle, 60 degree, Orthocenter, Congruence, Midpoint.
 

Proposed Problem 125. Area of Triangle, Star, Trisection of Sides.
Midpoints.

Proposed Problem 124. Area of triangle, Similarity, Trisection of Sides. Midpoints.

Proposed Problem 123. Area of triangle, Similarity, Trisection of Sides. Midpoints.

Proposed Problem 122. Marion Walter's Theorem. Area of triangle and Hexagon, Trisection of Sides. Midpoints.

Proposed Problem 121. Similarity and Area of triangle, Trisection of Sides.
Midpoints.

Proposed Problem 108. Angles, Triangle, Median. Midpoints.

Proposed Problem 98. Quadrilateral Area, Centroid, Similarity.
Midpoints.

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Proposed Problem 89. Triangles of equal area, Midpoints.

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

Proposed Problem 87. Area of Quadrilaterals and Midpoints of Diagonals.

Proposed Problem 1: Angles of a Triangle. Midpoint, Congruence. Hints are provided.

Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

Proposed Problem 65: Right Triangle, Mindpoints.

Proposed Problem 61: Triangle, Trisection of Sides. Midpoints.

Proposed Problem 59: Right and Equilateral Triangles, Midpoints

Generalizing Van Aubel: Michael de Villiers' Theorems.
Midpoints. 

Proposed Problem 47. Angles and triangles.
Midpoints.

Proposed Problem 46. Angles and triangles. Midpoints.

Triangle and Squares 16
Midpoints.

Triangle and Squares 12.
Midpoints.

Triangle and Squares 11.
Midpoints.

Triangle and Squares 7
Midpoints.

Triangle and Squares 5
Midpoints.

Triangle and Squares 4
Midpoints.

Triangle and Squares 2
Midpoints.

Geometry Online Glossary. Collinear Points.
Geometry Glossary based on the new New York State mathematics standards initiative.

Interactive Geometry Glossary using AnswerTips technology.
Nonagon or Enneagon.