Online Geometry: Transversal Line, Theorems and Problems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Proposed Problem 354.
Rhombus, Square, 45 degrees.

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

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

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

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

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

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

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

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

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

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

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

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

Six Tangential or Circumscribed Quadrilaterals Theorem.

Proposed Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

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

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

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

Proposed Problem 286: Square, Midpoints, Octagon.

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 235. Parallelogram, Transversal line, Perpendicular lines.

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

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

Proposed Problem 232. Parallelogram, Line through a vertex, 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.

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

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

Proposed Problem 226. Triangle, Centroid, Perpendicular lines.

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

Proposed Problem 219. Rhombus, Perpendiculars, Arithmetic Mean.

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

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

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

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

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

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

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

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

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

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

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

Proposed Problem 162. Parallelogram, Triangles, Areas.  

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

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

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

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

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

Proposed Problem 149. Quadrilateral, Area, Midpoints.

Proposed Problem 148. Quadrilateral, Area, Midpoints.

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

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

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

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

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

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

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

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

Proposed 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.

Proposed Problem 96. Similar Triangles, Incenters, Parallelogram.

Proposed Problem 95. Similar Triangles, Inradii, Parallel.

Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii.

Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram.

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

Proposed Problem 91. Similar Triangles, Altitude, Parallel.

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 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

Proposed Problem 64: Triangle, Incircle, Transversal.

Proposed Problem 61: Triangle, Trisection of Sides