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

Quadrilaterals: Theorems and Problems
3




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

Geometry Problem 832
Quadrilateral, Isosceles triangle, 707040 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. 
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