Quadrilaterals, Theorems and Problems Index. Page 1 of 4

Quadrilaterals: Table of Content (Page 1 of 4)

Parallelograms Index.

Word Cloud of Quadrilateral.
Visual Summary.

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
 

Complete Quadrilateral Index.
 

Equilic Quadrilateral.
 

Triangle and Squares. 21 theorems. Visual illustrations.

Golden Rectangles.

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.

Montessori Method: Geometric solid bases, Rectangle, Square, Circle for Children.

Geometry Problem 873
Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence.

Geometry Problem 872
Quadrilateral, Triangle, Angle, 30, 90 degrees.

Geometry Problem 856
Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 855
Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 832
Quadrilateral, Isosceles triangle, 70-70-40 degrees, Congruence, Auxiliary lines, Equilateral triangle.

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

Geometry Problem 830
Quadrilateral, Triangle, Angles, 30 degrees, Congruence.

Geometry Problem 828
Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian.

Geometry Problem 819.
Quadrilateral, Triangle, Angles, 30 degrees.

Geometry Problem 748.
Quadrilateral, 90 Degrees, Diagonal, Perpendicular, Metric Relations.

Geometry Problem 698.
Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Geometry Problem 695.
Triangle, Quadrilateral, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Geometry Problem 615
Right Triangle with a Square, Diagonals, Center, Area of Quadrilateral.

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

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

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

Problem 582.
Quadrilateral, Diagonals, Incenters, Metric Relations.

Problem 579.
Quadrilateral, Diagonals, Triangles, Areas.

Problem 556.
Quadrilateral, Diagonal, Angles, Auxiliary Lines.

Problem 521.
Triangle with three Squares, Altitude, Rectangle, Area.

Puzzle: Geometry Problems 161 - 170. 22 piece polygons.
Area, Triangle, Parallelogram, Trapezoid, Pentagon, Diagonal, Midpoint, Octagon.

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

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence.

Problem 529.
Right Trapezoid, Circle, Diameter.

Problem 520.
Triangle with six Squares, Ratio, Area.

Problem 519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area.

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

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

Problem 517.
Right Triangle, Six Squares, Areas.

Problem 514.
Triangle, Five Squares, Line, Area.

Geometry Problems 181 - 190.
Right Triangle, Trapezoid, Square, Intersecting Circles, Circular Sector, 90 Degrees, Angles, Trisection, Hypotenuse, Distance, Incenter, Altitude, Diagonal, 45 Degrees, Tangent, Chord, Perpendicular.

Problem 512.
Triangle with three squares and concurrency.

Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.

Geometry Problems 151 - 160.
Triangle, Quadrilateral, Area, Trisection, Circle, Proportion, Diagonal, Chord,Inradius, Circumradius, Exradius, Euler, distance, Incenter, Circumcenter, Excenter, Incircle, Circumcircle.

Problem 508.
Triangle with three Squares, Four triangle of equal Area.

Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.

Geometry Problems 141 - 150.
Triangle, Quadrilateral, Parallelogram, Incircle, Incenter, Tangent, Parallel, Perimeter, Area, Inradius, Circumradius, Midpoint, Varignon, Trisection.

Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.

Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.

Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees.

Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel.

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius.

Problem 489.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

Problem 483.
Square, Angle, 90 degrees, Measurement.

Problem 477.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

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

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

Proposed Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement.

Proposed Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees.

Proposed Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

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

Vecten Outer Point.
 

Proposed Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts.

Proposed Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

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.

Congruence. Index.

Similarity, Ratios, Proportions. Index.

Areas Index.

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