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Quadrilaterals: Table of Content
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Word Cloud of Quadrilateral.
Visual Summary. |
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Parallelograms
Index.
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Square. |
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Area
of a Square Index.
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Rectangle.
Theorems and Problems Index. |
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Rhombus.
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Trapezoids.
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Median of a Trapezoid, Theorems and Problems.
Index.
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Cyclic Quadrilateral.
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Tangential
or Circumscribed Quadrilateral
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Equilic Quadrilateral.
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Triangle and Squares. 21
theorems. Visual illustrations. |
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IC 4406: A Seemingly Square Nebula,
Evidence indicates that IC 4406 is likely a hollow cylinder, with its square appearance the result of our vantage point in viewing the cylinder from the side.
Credit: C. R. O'Dell (Vanderbilt U.) et al., Hubble Heritage Team, NASA |
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Tangential or Circumscribed Quadrilateral:
Diagonals, Inradii Theorem. |
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Tangential or Circumscribed Quadrilateral:
Pitot Theorem. |
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Six Tangential or Circumscribed Quadrilaterals Theorem. |
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Proposed
Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees. |
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Proposed
Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity. |
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Proposed
Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
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Proposed
Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal. |
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Proposed
Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal. |
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Proposed
Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence. |
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Proposed
Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence. |
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Proposed
Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence. |
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Proposed
Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint. |
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Proposed Problem
337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points. |
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Proposed Problem
336.
Two equal circles, a Common Tangent and a Square. |
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Proposed Problem
335.
Cyclic Quadrilateral, Perpendiculars to Sides. |
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Proposed Problem
334.
Cyclic Quadrilateral, Perpendiculars to Diagonals. |
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Proposed Problem
331.
Square, Point on the Inscribed Circle, Tangency Points. |
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Proposed Problem
330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter. |
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Proposed Problem
324.
Quadrilateral with perpendicular diagonals, Concurrence. |
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Proposed Problem
322.
Square, Inscribed circle, Tangent, Triangle area. |
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Proposed Problem
317.
Right triangle and Inscribed Squares. |
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Proposed Problem
316.
Circular segments and Inscribed Squares. |
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Proposed Problem
313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean. |
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Proposed Problem
312.
Cyclic quadrilateral, Side extensions, Tangents. |
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Proposed Problem
280.
Quadrilateral, Perpendiculars, Area of Squares. |
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Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
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Proposed Problem
252.
Parallelogram, sides, diagonals, squares, areas.
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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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Composition II in Red, Blue, and Yellow by Piet Mondrian, pioneer of Geometric abstraction.
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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
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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Proposed Problem
232. Parallelogram, Line through a vertex, 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, Perpendiculars. |
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Proposed Problem
225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance. |
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Proposed Problem
219. Rhombus, perpendiculars, arithmetic mean.
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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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Classical Theorems.
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Sol
LeWitt Drawings: A square.
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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
198. Triangle, Quadrilateral, Angles.
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Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas.
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Proposed Problem
189. Squares, Distances. |
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Proposed Problem
188. Square, Diagonal, 45 Degrees Angle. |
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Proposed Problem
185. Trapezoid, Triangles and Angles. |
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Proposed Problem
184. Triangle and Angles. |
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Proposed Problem
181. Circular Sector of 90 degrees, find an angle. |
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Proposed Problem
179. Rhombus, Square, Diagonal, Angle. |
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Proposed Problem
178. Quadrilateral, Trisection of sides, Area.
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Proposed Problem
177. Parallelogram with Midpoints,
Triangles, Areas. |
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Proposed Problem
176. Quadrilateral with Midpoints,
Triangles, Areas.
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Proposed Problem
175. Quadrilateral with Midpoints, Areas.
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Proposed Problem
174. Quadrilateral with Midpoints, Triangles, Areas.
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Proposed Problem
173. Quadrilateral with Midpoints, Triangles, Areas.
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Proposed Problem
172. Trapezoid, Midpoints, Quadrilaterals, Areas.
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Proposed Problem
171. Trapezoid, Midpoints, Triangles, Areas.
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Proposed Problem
170. Trapezoid, Midpoint, Triangle, Area.
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Proposed Problem
169. Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas
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Proposed Problem
168. Parallelogram, Diagonal, Triangles,
Pentagon, Areas.
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Proposed Problem
167. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
166. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
165. Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem
164. Parallelogram, Trapezoid, Diagonal, Triangles, Areas.
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Proposed Problem
163. Trapezoid, Diagonals, Triangles, Areas.
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Proposed Problem
162. Parallelogram, Triangles, Areas.
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Proposed Problem
161. Parallelogram, Midpoints, Octagon, Areas.
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Congruence.
Index.
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Similarity, Ratios, Proportions.
Index.
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Areas Index. |