![Go Geometry: Quadrilaterals](../machu_picchu_h1_728x90.jpg)
The Incas used trapezoids for all their windows and doors, which withstand
earthquakes well.
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Quadrilaterals: Theorems and Problems
2
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![](../circle/brahmagupta_theorem_170.jpg) |
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![Geometry problem 1182](../school-college/2/p1182-two-squares-sum-areas-metric-relations-1.jpg) |
Geometry Problem 1182
Two Squares, Four Quadrilaterals, Sum of the Areas, Metric Relations. |
![Geometry problem 1181](../school-college/2/p1181-quadrilateral-tangential-cyclic-diameter-problem-solving-1.jpg) |
Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter. |
![Geometry problem 1180](../school-college/2/p1180-triangle-quadrilateral-120-degrees-bisector-1.jpg) |
Geometry Problem 1180
Quadrilateral, 120 Degrees, Diagonals, Perpendicular. |
![Geometry problem 1176](../school-college/2/p1176-cyclic-quadrilateral-circle-diameter-collinear-concurrent-1.jpg) |
Geometry Problem 1176
Cyclic Quadrilateral, Diagonals, Six Diameters, Circles, Collinear Points, Concurrent Lines. |
![Six Tangential Quadrilaterals Theorem, problem 1175](../geometry/six_quadrilateral_17.jpg) |
Geometry Problem 1175: Six Tangential or Circumscribed Quadrilaterals Theorem |
![Geometry problem 1174](../school-college/2/p1174-triangle-double-triple-angle-bisector-problem-solving-1.jpg) |
Geometry Problem 1174
Triangle, Quadrilateral, Double, Triple, Angle, Congruence, Excenter, Angle Bisector. |
![Geometry problem 1152](../school-college/2/p1152-triangle-quadrilateral-10-20-30-degrees-angle-problem-solving-1.jpg) |
Geometry Problem 1152.
Triangle, Quadrilateral, Angle, 10, 20, 30 Degrees. |
![Geometry problem 1130](../school-college/2/p1130-cyclic-quadrilateral-diagonal-angle-bisector-congruence-1.jpg) |
Geometry Problem 1130.
Cyclic Quadrilateral, Diagonals, Angle Bisector, Congruent Angles. |
![Geometry Problem 1119](../school-college/2/p1119-quadrilateral-similar-triangle-midpoint-ratio-angle-math-1.jpg) |
Geometry Problem
1119.
Quadrilateral, Similar Triangles, Midpoints, Equal Ratio, Angles. |
![Geometry Problem 1097](../school-college/1/p1097-quadrilateral-area-inscribed-circle-radius-90-degree-1.jpg) |
Geometry Problem
1097.
Quadrilateral, Inscribed Circle, 90 Degree, Angle, Area. |
![Geometry Problem 1079](../school-college/1/p1079-isosceles-triangle-quadrilateral-double-angle-class-math-1.jpg) |
Geometry Problem
1079.
Quadrilateral, Isosceles Triangle, Diagonals, Double Angle. |
![Geometry Problem 1075](../school-college/1/p1075-triangle-90-degrees-quadrilateral-midpoint-distance-geometry-math-1.jpg) |
Geometry Problem
1075.
Quadrilateral, Right Triangle, 90 Degrees, Isosceles, Midpoint, Distance. |
![Geometry Problem 1074](../school-college/1/p1074-triangle-90-30-15-45-degrees-angle-geometry-math-1.jpg) |
Geometry Problem
1074.
Quadrilateral, Right Triangle, Angles, 15, 22,5, 30, 90 Degrees. |
![Geometry Problem 1052](../school-college/1/p1052-quadrilateral-three-circumcircles-concyclic-points-math-1.jpg) |
Geometry Problem
1052.
Triangle, Quadrilateral, Three Circumcircles, Circle, Concyclic Points, Cyclic Quadrilateral. |
![Geometry Problem 1046](../school-college/1/p1046-rectangle-circumcircle-radius-square-metric-relations-math-1.jpg) |
Geometry Problem
1046.
Rectangle, Circle, Circumradius, Metric Relations. |
![Geometry Problem 1045](../school-college/1/p1045-quadrilateral-trinagle-triple-angle-congruence-math-1.jpg) |
Geometry Problem
1045.
Quadrilateral, Diagonal, Triple Angle, Triangle, Congruence. |
![Geometry Problem 1041](../school-college/1/p1041-quadrilateral-perpendicular-diagonals-congruence-metric-relations-math-1.jpg) |
Geometry Problem
1041.
Quadrilateral, Perpendicular, Diagonals, Congruence, Metric Relations. |
![Geometry Problem 1030](../school-college/1/p1030-quadrilateral-triangle-area-midpoint-parallel-online-math-1.jpg) |
Geometry Problem
1030.
Quadrilateral, Triangle, Area, Midpoint, Parallel lines. |
![Geometry Problem 1016](../school-college/1/p1016-triangle-45-degrees-angle-altitude-bisector-quadrilateral-area-math-1.jpg) |
Geometry Problem
1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector. |
![Geometry Problem 1015](../school-college/1/p1015-right-triangle-square-altitude-metric-relations-math-1.jpg) |
Geometry Problem
1015.
Right Triangle, Square, Altitude, Metric Relations. |
![Geometry Problem 1014](../school-college/1/p1014-square-45-degree-angle-diagonal-area-math-1.jpg) |
Geometry Problem
1014.
Square, Diagonal, 45 Degrees, Angle, Equal Areas, Triangle, Quadrilateral. |
![Geometry Problem 995](../school-college/p995-quadrilateral-perpendicular-diagonal-bisector-parallel-1.jpg) |
Geometry Problem 995.
Quadrilateral, Perpendicular Diagonals, Perpendicular Bisector, Parallel. |
![Geometry Problem 961](../school-college/p961-quadrilateral-trisect-side-sum-areas-1.jpg) |
Geometry Problem 961.
Quadrilateral, Trisection, Sides, Sum of Areas. |
![Geometry Problem 960](../school-college/p960-quadrilateral-trisect-side-congruence-similarity-1.jpg) |
Geometry Problem 960.
Quadrilateral, Trisection, Sides, Congruence, Similarity, Triangle. |
![Geometry Problem 955](../school-college/p955-quadrilateral-diagonal-angle-30-40-60-70-degrees-1.jpg) |
Geometry Problem 955.
Quadrilateral, Triangle, Diagonals, Triangle, Angles, 30, 40, 60, 70 Degrees. |
![Geometry Problem 946](../school-college/p946-quadrilateral-diagonal-midpoint-parallel-area-1.jpg) |
Geometry Problem 946.
Triangle, Quadrilateral, Area, Diagonal, Midpoint, Parallel. |
![Problem 925](../school-college/p925-cyclic-quadrilateral-diagonal-angle-bisector-parallel-1.jpg) |
Geometry Problem 925.
Cyclic Quadrilateral, Diagonal, Circle, Angle Bisector, Parallel.
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![Problem 924](../school-college/p924-quadrilateral-perpendicular-circle-chord-tangent-midpoint-metric-relation-1.jpg) |
Geometry Problem 924.
Quadrilateral, Diagonal, Perpendicular, Circle, Tangent, Midpoint, Metric Relations.
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![Problem 923](../school-college/p923-infographic-quadrilateral-obtuse-inequality-diagonal-1.jpg) |
Geometry Problem 923.
Quadrilateral, Quadrangle, Obtuse Angle, Triangle, Diagonal, Inequality, Length.
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![Problem 910](../school-college/p910-bicentric-quadrilateral-incenter-circumcenter-distance-circumradius-1.jpg) |
Geometry Problem 910.
Bicentric Quadrilateral, Distance between the Incenter and Circumcenter, Incircle, Circumcircle, Circumscribed, Inscribed, Circumradius.
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![Problem 909 Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius](../school-college/p909-bicentric-quadrilateral-incenter-distance-circle-inradius-1.jpg) |
Geometry Problem 909.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius,
Distance.
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![Problem 908 Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius](../school-college/p908-bicentric-quadrilateral-tangent-circle-inradius-1.jpg) |
Geometry Problem 908.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.
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![Problem 907 Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius](../school-college/p907-bicentric-quadrilateral-tangent-circle-inradius-1.jpg) |
Geometry Problem 907.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.
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![Problem 906 Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Perpendicular](../school-college/p906-bicentric-quadrilateral-chord-perpendicular-1.jpg) |
Geometry Problem 906.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Perpendicular.
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![Geometry Problem 873: Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence](../school-college/p873-quadrilateral-diagonal-angle-bisector-triangle-1.jpg) |
Geometry Problem 873
Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence. |
![Geometry Problem 872: Quadrilateral, Triangle, Angle, 30, 90 degrees](../school-college/p872-angle-30-degrees-triangle-quadrilateral-1.jpg) |
Geometry Problem 872
Quadrilateral, Triangle, Angle, 30, 90 degrees. |
![Problem 856: Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines](../school-college/p856-quadrilateral-triangle-angle-30-degrees-diagonal-1.jpg) |
Geometry Problem 856
Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines. |
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