Parallelogram, Theorems and Problems - Table of Content

Parallelogram Definition.

Square.
Theorems and Problems Index.

Rectangle.
Theorems and Problems Index.

Area of a Parallelogram.
Theorems and Problems Index.

Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area.

Geometry Problem 865
Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity.

Geometry Problem 864
Parallelogram, Diagonal, Congruence, Similarity, Metric Relations.

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.

Geometry Problem 840
Parallelogram, Perpendicular, Diagonal, Metric Relations, Similarity.

Geometry Problem 839
Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 838
Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 836
Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations.

Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional.

Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion.

Geometry Problem 831
Quadrilateral, Diagonal, Midpoint, Opposite Angles, Congruence, Parallelogram.

Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter.

Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter.

Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle.

Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles.

Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram.

Geometry Problem 771
Area of a Parallelogram, Star, Pentagon, Triangles.

Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement.

Geometry Problem 768
Parallelogram with Equilateral Triangles on Sides.

Geometry Problem 763
Parallelogram, Diagonal, Parallel, Congruence.

Geometry Problem 762
Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle.

Geometry Problem 751.
Parallelogram, Congruence, Intersecting Lines, Angle Bisector.

Geometry Problem 744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations.

Geometry Problem 732.
Triangle, Altitude, Orthic Triangle, Orthocenter, Congruence, Parallelogram.

Geometry Problem 731.
Cyclic quadrilateral, Triangle, Orthocenter, Altitude, Perpendicular, Parallelogram.

Geometry Problem 710.
Parallelogram, Midpoint, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence.

Geometry Problem 709.
Parallelogram, Midpoint, Diagonal, Metric Relations, Triangle.

Geometry Problem 677.
Parallelogram, Midpoint, Diagonal, Metric Relations.

Geometry Problem 661.
Intersecting Circles, Centers, Secant, Parallelogram.

Geometry Problem 659.
Parallelogram, Parallel Lines, Collinear Points.

Geometry Problem 621
Three Rectangles, Diagonals, Centers, Angles.

Geometry Problem 616
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Geometry Problem 614
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Geometry Problem 604
Parallelograms, Triangle, Trapezoid, Area.

Geometry Problem 603
Parallelogram, Diagonals, Congruence, Concurrency.

Geometry Problem 601
Cyclic Quadrilateral, Incenter, Excenter, Rectangle.

Problem 584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.

Problem 583.
Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas.

Problem 537.
Rectangle, Midpoints, Diagonal, Angle Bisector.

Problem 518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure.

Problem 489.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 477.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity.

Problem 470.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

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

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

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

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

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

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

Proposed Problem 354.
Rhombus, Square, 45 degrees.

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

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

Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity. Parallelogram.

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

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 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 219. Rhombus, perpendiculars, arithmetic mean.

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

Proposed Problem 189. Squares, Distances.

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

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

Proposed Problem 177. Parallelogram with 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 162. Parallelogram, Triangles, Areas.

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

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

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

Triangle and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Bottema's Theorem: Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Machu Picchu and Golden Rectangle.

Parallelogram Problem 96. Similar Triangles, Incenters, Parallelogram.

Parallelogram Problem 93. Similar Triangles, Circumcircles, Parallelogram.

Square
Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector. 

Proposed Problem 70: Squares inscribed in a triangle, Similarity.

Proposed Problem 69: Square inscribed in a triangle, Similarity.

Proposed Problem 62: Square Diagonal, Inscribed Circle.

Triangle and Squares. 21 theorems. Visual illustrations.

Generalizing Van Aubel: Michael de Villiers' Theorems.
 

Eyeball Theorem: Animated Angle to Geometry Study.

Hippocrates and Squaring the Circle
 

Triangle with Squares Problem

Thébault's Theorem. Parallelogram with Squares theorem
 

Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and trisection points of the edges.

Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.
 

Ptolemy's Theorem.
 

Cyclic Quadrilateral: Ratio of the Diagonals
 

Sangaku Problem. The incenters of four triangles in a cyclic quadrilateral form a rectangle.

Proposed Problem 35.
Incenters and Inradii in Cyclic Quadrilateral.