Machu Picchu, Geometry Theorems and Problems, Online Education

Geometry Theorems and Problems - Recent Additions (Page 11 of 15)

Euclidean Geometry

Elearning 190 tangent circles, chord, perpendicular

Proposed Problem 190. Tangent circles, Tangent chord, Perpendicular, Distance.  

Elearning 189

Proposed Problem 189. Squares, Distances.  

Elearning 188

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

Elearning 187: Right triangle, incircles, angles

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

Elearning 186: Right triangle, circles

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

Elearning 186: Right triangle, circles

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

Trapezoid and triangle problem

Proposed Problem 185. Trapezoid, Triangles and Angles.  

Elearning: Triangle, Angle

Proposed Problem 184. Triangle and Angles.  

Right triangle, Hypotenuse trisection

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

Overlapping circles, Angle

Proposed Problem 182. Overlapping Circles, Find an angle.  

Circular Sector 90 degree

Proposed Problem 181. Circular Sector of 90 degrees, find an angle.  

Circle tangent externally, trapezoid, area

Proposed Problem 180. Circles Tangent Externally, Common External Tangents, Areas.  

Rhombus, Square, Angle

Proposed Problem 179. Rhombus, Square, Diagonal, Angle.  

Geometry problem 178 Quadrilateral area

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

Elearning 177: Parallelogram with midpoints, Area

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

Elearning 176: Quadrilateral Area Problem

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

Elearning 175: Quadrilateral Area Problem

Proposed Problem 175. Quadrilateral with Midpoints, Areas.  

Quadrilateral with Midpoints, Triangles Area

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

Quadrilateral with Midpoints, Triangles Area

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

Elearning 172: Trapezoid, Quadrilateral, Area

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

Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas

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

Trapezoid, Triangle, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Elearning 165: Parallelogram area

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

Elearning 164: Parallelogram, Triangles, Area

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

Elearning 163 Trapezoid, Triangles, Area

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

Elearning 162 Parallelogram and Triangles Areas

Proposed Problem 162. Parallelogram, Triangles, Areas.  

Elearning 161 Parallelogram and Octagon Areas

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

Elearning: Triangle, Circle, Incircle, Radius

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

Triangle Elearning 159

Proposed Problem 159. Distances from the Circumcenter to the Incenter and the Excenters.  

Geometry Problem 158

Proposed Problem 158. Relation between the Circumradius, Inradius and Exradii of a triangle.  

Areas

Areas Index.

Congruence

Congruence. Index.

Similarity

Similarity, Ratios, Proportions. Index.

Elearning triangle 157

Proposed Problem 157. Distance from the Circumcenter to the Excenter.  

Elearning triangle 156

Proposed Problem 156. Triangle, Circumradius, Exradius, Chord, Secant line.  

Elearning 155

Proposed Problem 155. Euler's Theorem: Distance from the Incenter to the Circumcenter.  

Elearning 154

Proposed Problem 154. Triangle, Inradius, Circumradius, Chord.

Circumscribed quadrilateral

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

Circumscribed Quadrilateral

Proposed Problem 152. Circumscribed Quadrilateral, Diagonal, Chord, Proportion.  

Quadrilateral area, trisection

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

Quadrilateral area, trisection

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

Quadrilateral Area, Midpoint, Elearning

Proposed Problem 149. Quadrilateral, Area, Midpoints.

Quadrilateral area, Midpoint, Elearning

Proposed Problem 148. Quadrilateral, Area, Midpoints.

Quadrilateral Area, Elearning

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

Quadrilateral Area, Midpoint

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

Geometry Problem 145. Elearning Triangle

Proposed Problem 145. Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.  

Geometry problem 144 Triangle

Proposed Problem 144. Four Triangles, Incircle, Tangent and Parallel to Side, Inradii.

Geometry problem 143

Proposed Problem 143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.

Elearning 142: Triangle area

Proposed Problem 142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.

Elearning 141

Proposed Problem 141. Triangle, Incircle, Tangent , Parallel, Perimeters.

Elearning 140

Proposed Problem 140. Triangle, Excircle, Tangent, Semiperimeter.

Elearning 139: Triangle Area

Proposed Problem 139. Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.  

Nagel Theorem

Proposed Problem 138. Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.  

Geometry Problem 137

Proposed Problem 137. Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.  

Geometry Problem 136

Proposed Problem 136. Orthic Triangle, Altitudes, Perpendicular, Concyclic Points.  

Geometry Problem 135

Proposed Problem 135. Orthic Triangle, Altitudes, Perpendicular, Parallel  

Geometry Problem 134

Proposed Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Pappus Theorem

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

Gergonne Line

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

Interactive Simson Line

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

Elearning Geometry

Triangle, Medians, Six Circumcenters Concyclic. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Trapezoid

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

Interactive Geometry

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Problem 133

Proposed Problem 133. Triangle, Angle Bisectors, Collinear Points.

Triangles. Theorems and problems about triangles.

Circles. Theorems and problems about circles.

Triangle Centers.

Archimedes' Book of Lemmas

Quadrilaterals.

Adams' Circle Theorem.

First Ajima-Malfatti Point.

Second Ajima-Malfatti Point.

Apollonius' Tangency Problem for Three Circles Illustration with animation.

The Bevan Point.

Heron's Formula. Key facts and a purely geometric step-by-step proof.

Johnson: Intersecting circles

Johnson Theorem.

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

Langley's Problem Adventitious angles. 20 isosceles triangle with animation.
 

Lemoine Theorem

Menelaus' Theorem.

Miquel's Pentagram Theorem

Miquel's Pentagram Theorem Interactive proof with animation and key theorems.
 

Miquel's Pentagram with Dynamic Geometry. You can alter the pentagram 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.

Monge & d'Alembert Three Circles Theorem II 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.

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.

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