Geometry Theorems and Problems - Recent Additions (Page
10 of 15)
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Proposed Problem
281.
Triangles, Angles, Isosceles, Equilateral. |
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Cyclic Quadrilateral.
Index |
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Angle Bisector.
Index. |
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Angles. |
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Proposed Problem
280.
Quadrilateral, Perpendiculars, Area of Squares. |
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Polygon Classification. Interactive Mind Map. |
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Sacred
Geometry.
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Proposed Problem
279.
Tangent Circles, Common External Tangent, Chords, Inradius. |
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Proposed Problem
278.
Tangent Circles, Common External Tangent, Chord. |
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Proposed Problem
277.
Tangent Circles, Common External Tangent. |
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Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius. |
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Proposed Problem
275.
Right Triangle, Circumcircle, Sagitta, Inradius. |
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Sagitta, Arc, Chord. |
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Book I,
Proposition 9: Bisect a given angle
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Proposed Problem
274.
Isosceles Triangle, 80-80-20, Angles. |
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Isosceles Triangle. |
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Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
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Proposed Problem
272.
Tangent Circles, the Cube of the Common external tangent. |
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Rhombus.
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Proposed Problem
271.
Tangent Circles, the Cube of the Common external tangent. |
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Heptagons. |
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Classical Theorems.
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Heptagon and Heptagrams / Septegram.
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Proposed Problem
270.
Tangent Circles, Common external tangent, Fractional exponents. |
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Circumcenter.
Index.
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Pi
Day.
Saturday, March 14, 2009 = 3.14
It's time to get irrational. Tomorrow is Pi Day, when mathematicians will gather to celebrate the mystery of science's most famous strange number. |
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Proposed Problem
269.
Right Triangle, Altitude, Perpendicular, Projection. |
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Proposed Problem
268.
Right Triangle, Catheti and Altitude. |
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Proposed Problem
267.
Right Triangle, Product of Catheti. |
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Proposed Problem
266.
Right Triangle, Altitude, Geometric Mean. |
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Albert Einstein
and the Pythagorean theorem.
A preteen Albert Einstein devised a new proof of the Pythagorean theorem. |
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Proposed Problem
265.
Right Triangle, Pythagorean Theorem. |
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Proposed Problem
264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean. |
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Proposed Problem
263.
Triangle, Median, Altitude, Orthogonal Projection, Sides. |
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Proposed Problem
262.
Regular Hexagon inscribed in a circle, sum of distances. |
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Hexagons. |
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Proposed Problem
261.
Regular Pentagon inscribed in a circle, sum of distances.
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Pentagons. |
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Orthocenter
Index.
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Centroid
/Barycenter.
Index.
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Proposed Problem
260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.
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Proposed Problem
259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.
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Proposed Problem
258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
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Proposed Problem
255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
253.
Triangle, Centroid, Vertices, Distances, Squares.
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Equilateral Triangles Index. |
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Proposed Problem
252.
Rectangle, isosceles right triangle, square, area.
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Proposed Problem
251.
Parallelogram, sides, diagonals, squares, areas.
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Proposed Problem
250.
Quadrilateral, sides, diagonals, midpoints, squares.
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Proposed Problem
249.
Triangle sides, medians, squares.
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Median length, Apollonius' Theorem |
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Euclid's Elements Book II, Proposition 12: Law of Cosines.
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Euclid's Elements Book II, Proposition 13: Law of Cosines.
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Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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Proposed Problem
247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon
triangle.
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Proposed Problem
246.
Napoleon's Theorem I. External Equilateral triangles. |
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Proposed Problem
245. Parallelogram with Equilateral triangles
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Proposed Problem
244. Square, Diagonals, Centers, Distance.
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Proposed Problem
243. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
242. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
241. Triangle with Equilateral triangles, Congruence.
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Proposed Problem
240. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.
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Proposed Problem
238. Square, Midpoints, Lines, Congruence.
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Proposed Problem
237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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Proposed Problem
236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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Proposed Problem
235. Parallelogram, Transversal line, Perpendicular lines.
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Proposed Problem
234. Parallelogram, Line through a vertex, Perpendicular lines.
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Proposed Problem
233. Parallelogram, Exterior line, Perpendicular lines.
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Parallelograms
Index.
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Proposed Problem
232. Parallelogram, Line through a vertex, Perpendicular lines.
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Geometry Online
Glossary .
Geometry Glossary based on the new New York State
mathematics standards initiative. |
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Proposed Problem
231. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
230. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
229. Triangle, Centroid, Transversal, Perpendicular lines. |
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Proposed Problem
228. Triangle, Midpoints, Exterior line, Perpendiculars lines.
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Proposed Problem
227. Triangle, Centroid, Exterior line, Perpendicular lines. |
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Proposed Problem
226. Triangle, Centroid, Perpendicular lines. |
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Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon,
Apothem, Distance. |
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Proposed Problem 224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. |
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Proposed Problem 223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. |
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Proposed Problem 222. Viviani's theorem, Equilateral triangle,
Exterior point, Distances. |
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Proposed Problem 221. Viviani's theorem, Equilateral triangle,
Interior point, Distances. |
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Lune of Hippocrates Index.
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Proposed Problem 220. Right Triangle, Altitude, Angle Bisector,
Distance, Arithmetic Mean.
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Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.
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Proposed Problem 218. Right triangle, Altitude and Projections.
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Proposed Problem 217. Right triangle, Altitude and Projections.
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Proposed Problem 216. Quadrilateral, Angle Bisectors, and
Concurrency.
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Proposed Problem 215.
Quadrilateral, Angle Bisectors, and Cyclic
Quadrilateral.
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Proposed Problem 214.
Quadrilateral and Angle Bisectors.
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Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles,
Common Tangents. |
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Proposed Problem 212. 120 Degree Triangle, Equilateral triangles,
Areas.
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Archimedes Arbelos and Square 2.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem 211. 60 Degree Triangle, Equilateral triangles,
Areas.
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Proposed Problem 210. Triangle, Angles, Auxiliary Lines.
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Proposed Problem
209. Triangle, Incircles, Inradius. |
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Clifford's Circle Chain
Theorems. This is a step by step presentation of the first theorem.
Clifford discovered, in the ordinary Euclidean plane, a "sequence or
chain of theorems" of increasing complexity, each building on the last
in a natural progression.
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Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
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Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. |
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Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse. |
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Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
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Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. |
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Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. |
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Proposed Problem
202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius. |
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Proposed Problem 199. Triangle, Quadrilateral, Angles.
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Proposed Problem
198. Triangle, Quadrilateral, Angles.
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Proposed Problem
197. Area of a Triangle, Side, Inradius, and Exradius. |
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Proposed Problem
196. Triangle, Inradius and Exradii Formula. |
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Triangle Centers Index. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
194. Area of a Triangle, Semiperimeter, Exradius. |
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Proposed Problem
193. Area of a Triangle, Semiperimeter, Inradius. |
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Proposed Problem
192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.
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Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas.
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