Transversal Line, Theorems and Problems - Table of Content

Ceva's Theorem. Concurrency. Interactive proof with animation. Key concept: Menelaus Theorem. 

Menelaus' Theorem. Interactive proof with animation and key concepts.
Transversal line.

Pascal's Mystic Hexagram Theorem Proof
Transversal line.

Pappus Theorem. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Transversal line.

Angle between two Simson Lines. Proof with animation.
Transversal line. 

Simson Line. A proof of Simson line with animation.
Transversal line.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Transversal line.

Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
Transversal line. 

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

Monge & d'Alembert Three Circles Theorem I with Dynamic Geometry You can alter the geometric construction dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand. Requires Java Plug-in 1.3 or higher. Please be patient while the applet loads on your computer. If you are using a dial-up connection, it may take a few minutes but is well worth the wait. Cabri, GSP, Cinderella, C.a.R.

Gergonne Point Theorem. Concurrency. Interactive proof with animation.

Key concept: Ceva's Theorem.
 

Nagel Point Theorem. Proof.
 

Interactive Gergonne Line and Nobbs Points. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Transversal line.

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

Schiffler Point: Four Euler Lines with interactive animation and manipulation.

Lemoine Theorem

Complete Quadrilateral: Ortholine-Steiner Line.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation

Geometry Problem 824
Desargues' Theorem, Triangles in Perspective.

Geometry Problem 761
Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle.

Geometry Problem 798
Parallelogram, Secant Line, Transversal, Tangent Circles, Circumcircles, Triangle.

Geometry Problem 759
Equilateral Triangle, Transversal, Trisection of sides, Congruence, Angle.

Geometry Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence.

Geometry Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity.

Geometry Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal.

Geometry Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Proposed Problem 398.
Parallelogram, Area, Similarity, Congruence.

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

Geometry Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Geometry Problem 392.
Triangle, Parallel lines, Concurrent lines.

Geometry Problem 391.
Triangle, Parallel lines, Collinear points.

Geometry Problem 390.
Triangle, Parallel lines, Collinear points.

Geometry Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Geometry Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Geometry Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

Geometry Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Angles.

Geometry Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Geometry Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Geometry Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Geometry Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Geometry Problem 357.
Square, Exterior point, Triangles, Area.

Geometry Problem 354.
Rhombus, Square, 45 degrees.

Geometry Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Geometry Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Geometry Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

Geometry Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Geometry Problem 348.
Circles, Common External Tangents, Common Internal Tangent.

Geometry Problem 346.
Equal circles, Tangents, Hexagon, Semiperimeter.

Geometry Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Geometry Problem 344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter.

Geometry Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Geometry Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

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

Geometry Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Six Tangential or Circumscribed Quadrilaterals Theorem.

Geometry Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Geometry Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Geometry Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Geometry Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Geometry Problem 286: Square, Midpoints, Octagon.

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

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

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

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

Geometry Problem 235. Parallelogram, Transversal line, Perpendicular lines.

Geometry Problem 234. Parallelogram, Line through a vertex, Perpendicular lines.

Geometry Problem 233. Parallelogram, Exterior line, Perpendicular lines.

Geometry Problem 232. Parallelogram, Line through a vertex, Perpendicular lines.

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

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

Geometry Problem 229. Triangle, Centroid, Transversal, Perpendicular lines.

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

Geometry Problem 227. Triangle, Centroid, Exterior line, Perpendicular lines.

Geometry Problem 226. Triangle, Centroid, Perpendicular lines.

Geometry Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base.

Geometry Problem 219. Rhombus, Perpendiculars, Arithmetic Mean.

Geometry Problem 188. Square, Diagonal, 45 Degrees Angle.

Geometry Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.

Geometry Problem 186. Right Triangle, Altitude, Incenters, Circles.

Geometry Problem 178. Quadrilateral, Trisection of sides, Area.  

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

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

Geometry Problem 175. Quadrilateral with Midpoints, Areas.  

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

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

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

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

Geometry Problem 169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas.  

Geometry Problem 168. Parallelogram, Diagonal, Triangles, Pentagon, Areas.  

Geometry Problem 167. Parallelogram, Diagonal, Triangles, Areas.  

Geometry Problem 166. Parallelogram, Diagonal, Triangles, Areas.  

Geometry Problem 165. Parallelogram, Diagonal, Triangles, Areas.  

Geometry Problem 164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.  

Geometry Problem 163. Trapezoid, Diagonals, Triangles, Areas.  

Geometry Problem 162. Parallelogram, Triangles, Areas.  

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

Geometry Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.

Geometry Problem 153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.

Geometry Problem 151. Quadrilateral, Area, Trisection of Sides.

Geometry Problem 150. Quadrilateral, Area, Trisection of Sides.

Geometry Problem 149. Quadrilateral, Area, Midpoints.

Geometry Problem 148. Quadrilateral, Area, Midpoints.

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

Geometry Problem 131. Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.

Geometry Problem 130. Triangle, Concurrent Cevians, Sum of Ratios.

Geometry Problem 129. Triangle, Concurrent Cevians, Sum of Ratios.

Geometry Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

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

Geometry Problem 124. Area of triangle, Similarity, Trisection of Sides.

Geometry Problem 123. Area of triangle, Similarity, Trisection of Sides.

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

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

Proposed Problem 97. Similar Triangles, Areas.

Geometry Problem 96. Similar Triangles, Incenters, Parallelogram.

Geometry Problem 95. Similar Triangles, Inradii, Parallel.

Geometry Problem 94. Similar Triangles, Circumcircles, Circumradii.

Geometry Problem 93. Similar Triangles, Circumcircles, Parallelogram.

Geometry Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.

Geometry Problem 91. Similar Triangles, Altitude, Parallel.

Geometry Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Geometry Problem 89. Triangles of equal area, Midpoints.

Geometry Problem 88. Triangle and Quadrilateral Areas, Midpoints.

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

Geometry Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

Geometry Problem 64: Triangle, Incircle, Transversal.

Geometry Problem 61: Triangle, Trisection of Sides