The Incas used trapezoids for all their windows and doors, which withstand earthquakes well.

Quadrilaterals: Table of Content (Page 1 of 4)

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Word Cloud of Quadrilateral.
Visual Summary.

Parallelograms Index.

Square.

Area of a Square Index.

Rectangle. Theorems and Problems Index.

Rhombus.

Trapezoids.

Median of a Trapezoid, Theorems and Problems. Index.

Cyclic Quadrilateral.
 

Tangential or Circumscribed Quadrilateral
 

Equilic Quadrilateral.
 

Triangle and Squares. 21 theorems. Visual illustrations.

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

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Six Tangential or Circumscribed Quadrilaterals Theorem.

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

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

Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Proposed Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal.

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

Proposed Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence.

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Proposed Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Proposed Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Proposed Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

Proposed Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 316.
Circular segments and Inscribed Squares.

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Proposed Problem 312.
Cyclic quadrilateral, Side extensions, Tangents.

Proposed Problem 280.
Quadrilateral, Perpendiculars, Area of Squares.

Proposed Problem 273.
Triangle, Perpendiculars, Area of Squares.

Proposed Problem 252.
Parallelogram, sides, diagonals, squares, areas.

Proposed Problem 251.
Parallelogram, sides, diagonals, squares, areas.

Proposed Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.

Composition II in Red, Blue, and Yellow by Piet Mondrian, pioneer of Geometric abstraction.

Proposed Problem 245. Parallelogram with Equilateral triangles

Proposed Problem 244. Square, Diagonals, Centers, Distance.

Proposed Problem 243. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 242. Triangle with Equilateral triangles, Parallelogram.

Proposed Problem 240. Triangle with Equilateral triangles, Parallelogram.

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 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, Perpendiculars.

Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon, Apothem, Distance.

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Proposed Problem 214. Quadrilateral and Angle Bisectors.

Classical Theorems.

Sol LeWitt Drawings: A square.

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Proposed Problem 198. Triangle, Quadrilateral, Angles.

Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.

Proposed Problem 189. Squares, Distances.

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

Proposed Problem 185. Trapezoid, Triangles and Angles.

Proposed Problem 184. Triangle and Angles.

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

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

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 170. Trapezoid, Midpoint, Triangle, Area.

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.

Congruence. Index.

Similarity, Ratios, Proportions. Index.

Areas Index.