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

Quadrilaterals: Theorems and Problems 2

Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points.

Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram.

Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement.

Geometry Problem 1243.
Quadrilateral, Four Exterior Angle Bisectors, Semi-sum, Angles. Mobile Apps.

Geometry Problem 1242.
Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps.

Geometry Problem 1241.
Quadrilateral, Four Exterior Angle Bisectors, Cyclic Quadrilateral, Circle. Mobile Apps.

Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations.

Geometry Problem 1226
Quadrilateral, Squares, Centers, Midpoints, Congruence.

Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals.

Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas.

Geometry Problem 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel.

Geometry Problem 1188
Triangle, Parallelogram, Parallel Lines, Trapezoid, Area.

Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area.

Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area.

Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations.

Geometry Problem 1182
Two Squares, Four Quadrilaterals, Sum of the Areas, Metric Relations.

Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter.

Geometry Problem 1180
Quadrilateral, 120 Degrees, Diagonals, Perpendicular.

Geometry Problem 1176
Cyclic Quadrilateral, Diagonals, Six Diameters, Circles, Collinear Points, Concurrent Lines.

Geometry Problem 1175: Six Tangential or Circumscribed Quadrilaterals Theorem

Geometry Problem 1174
Triangle, Quadrilateral, Double, Triple, Angle, Congruence, Excenter, Angle Bisector.

Geometry Problem 1152.
Triangle, Quadrilateral, Angle, 10, 20, 30 Degrees.

Geometry Problem 1130.
Cyclic Quadrilateral, Diagonals, Angle Bisector, Congruent Angles.

Geometry Problem 1119.
Quadrilateral, Similar Triangles, Midpoints, Equal Ratio, Angles.

Geometry Problem 1097.
Quadrilateral, Inscribed Circle, 90 Degree, Angle, Area.

Geometry Problem 1079.
Quadrilateral, Isosceles Triangle, Diagonals, Double Angle.

Geometry Problem 1075.
Quadrilateral, Right Triangle, 90 Degrees, Isosceles, Midpoint, Distance.

Geometry Problem 1074.
Quadrilateral, Right Triangle, Angles, 15, 22,5, 30, 90 Degrees.

Geometry Problem 1052.
Triangle, Quadrilateral, Three Circumcircles, Circle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 1046.
Rectangle, Circle, Circumradius, Metric Relations.

Geometry Problem 1045.
Quadrilateral, Diagonal, Triple Angle, Triangle, Congruence.

Geometry Problem 1041.
Quadrilateral, Perpendicular, Diagonals, Congruence, Metric Relations.

Geometry Problem 1030.
Quadrilateral, Triangle, Area, Midpoint, Parallel lines.

Geometry Problem 1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector.

Geometry Problem 1015.
Right Triangle, Square, Altitude, Metric Relations.

Geometry Problem 1014.
Square, Diagonal, 45 Degrees, Angle, Equal Areas, Triangle, Quadrilateral.

Geometry Problem 995.
Quadrilateral, Perpendicular Diagonals, Perpendicular Bisector, Parallel.

Geometry Problem 961.
Quadrilateral, Trisection, Sides, Sum of Areas.

Geometry Problem 960.
Quadrilateral, Trisection, Sides, Congruence, Similarity, Triangle.

Geometry Problem 955.
Quadrilateral, Triangle, Diagonals, Triangle, Angles, 30, 40, 60, 70 Degrees.

Geometry Problem 946.
Triangle, Quadrilateral, Area, Diagonal, Midpoint, Parallel.

Geometry Problem 925.
Cyclic Quadrilateral, Diagonal, Circle, Angle Bisector, Parallel.

Geometry Problem 924.
Quadrilateral, Diagonal, Perpendicular, Circle, Tangent, Midpoint, Metric Relations.

Geometry Problem 923.
Quadrilateral, Quadrangle, Obtuse Angle, Triangle, Diagonal, Inequality, Length.

Geometry Problem 910.
Bicentric Quadrilateral, Distance between the Incenter and Circumcenter, Incircle, Circumcircle, Circumscribed, Inscribed, Circumradius.

Geometry Problem 909.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius, Distance.

Geometry Problem 908.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 907.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 906.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Perpendicular.

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.

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