![Go Geometry Education, Tutoring, Tutorial, Tutor](../problem/h_geometry_problem_810.jpg)
Quadrilaterals: Theorems and Problems
The Incas built their windows and doors in the shape of trapezoids, as this shape is known for its ability to withstand earthquakes well.
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![Quadrilateral Index](../geometry/quadrilateral_index_170.jpg) |
Four lines intersect,
Sides, angles, shapes perplex,
Quadrilateral quests. |
![Parallelograms Index](../geometry/parallelograms_17.jpg) |
Parallelograms Index.
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![Quadrilateral Word Cloud](../software/word_cloud_quadrilateral_1.jpg) |
Word Cloud of Quadrilateral.
Visual Summary. |
![Squares Index](../geometry/squares_index_17.jpg) |
Square. |
![Area of a square](../geometry/area_square_index_17.jpg) |
Area of a Square Index.
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![Rectangle Index](../geometry/rectangle_index_17.jpg) |
Rectangle. Theorems and Problems Index. |
![Rhombus, Rhombuses, Rhombi](../geometry/rhombus_index_17.jpg) |
Rhombus.
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![Trapezoid Index](../geometry/trapezoid_170.jpg) |
Trapezoids.
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![Trapezoid median, Theorems and Problems, Index](../geometry/trapezoid_median_index_17.jpg) |
Median of a Trapezoid, Theorems and Problems.
Index.
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![Cyclic Quadrilateral Index](../geometry/cyclic_quadrilateral_index_.jpg) |
Cyclic Quadrilateral.
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![Tangential or Circumscribed Quadrilateral Index, theorems and problems](../geometry/tangential_quadrilateral_17.jpg) |
Tangential or Circumscribed Quadrilateral
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![Kite Index](../math_geometry_online_courses/kite-index-1.jpg) |
Kite Index.
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![Complete quadrilateral](../geometry/complete_quadrilateral_inde.jpg) |
Complete Quadrilateral Index.
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![Equilic Quadrilateral](../geometry/equilic_quadrilateral_17.jpg) |
Equilic Quadrilateral.
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![](triangle_squares_sat170.jpg) |
Triangle and Squares. 21 theorems. Visual
illustrations. |
![van Aubel theorem for Tablets, iPad, Nexus, Galaxy](../geometry/van-aubel-theorem-quadrilateral-square-ipad-nexus-galaxy-1.jpg) |
van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation for Tablets, iPad,
Nexus, Galaxy. |
![Golden Rectangles Index](../wonder_world/golden_rectangle_index_17.jpg) |
Golden Rectangles. |
![](../equilic/cyclic_ptolemy_theorem_170.jpg) |
Ptolemy's Theorem.
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![Tangential Quadrilateral](../geometry/tangential_quadrilateral_1_.jpg) |
Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem. |
![Tangential Quadrilateral: Pitot Theorem](../geometry/pitot_theorem_17.jpg) |
Tangential or Circumscribed Quadrilateral: Pitot Theorem. |
![Geometry Problem 1570](../school-college/6/p1570-overlapping-two-squares-common-vertex-a-measures-class-1.jpg) |
Geometry Problem 1570:
Calculating BE in Overlapping Squares: A High School and College Geometry Challenge. |
![Geometry Problem 1569](../school-college/6/p1569-isosceles-triangle-square-relationship-diameter-incircle-tutoring-1.jpg) |
Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. |
![Geometry Problem 1568](../school-college/6/p1568-proving-concyclicity-in-triangle-with-incircle-and-tangent-circle-problem-solving-tutoring-1.jpg) |
Geometry Problem 1568:
Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle. |
![Geometry Problem 1567](../school-college/6/p1567-bases-isosceles-trapezoid-circumscribed-circle-chord-distance-measurement-tangent-tutoring-1.jpg) |
Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. |
![Geometry Problem 1564](../school-college/6/p1564-find-area-quadrilateral-in-right-triangle-abc-with-altitude-bisectors-midpoint-tutoring-1.jpg) |
Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1560](../school-college/6/p1560-trapezoid-ABCD-geometry-puzzle-angles-G-and-H-AGD-50-degrees-1.jpg) |
Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. |
![Geometry Problem 1543](../school-college/6/p1543-square-circle-arc-mindpoint-quadrilateral-area-school-college-1.jpg) |
Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. |
![Geometry Problem 1538](../school-college/6/p1538-triangle-external-squares-quadrilateral-area-segment-length-math-class-1.jpg) |
Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
![Geometry Problem 1537](../school-college/6/p1537-parallelogram-midpoint-triangle-area-intersection-math-challenge-1.jpg) |
Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
![Geometry Problem 1536](../school-college/6/p1536-quadrilateral-midpoint-area-triangle-math-education-1.jpg) |
Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
![Geometry Problem 1508](../school-college/6/p1508-isosceles-equilateral-triangle-angles-quadrilateral-60-80-degrees-1.jpg) |
Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. |
![Geometry Problem 1502](../school-college/6/p1502-rigth-triangle-incircles-measurement-inradius-square-quadrilateral-1.jpg) |
Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
![Geometry Problem 1501](../school-college/6/p1501-square-interior-point-distance-equal-angles-measurement-1.jpg) |
Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. |
![Dynamic Geometry 1481](../school-college/5/p1481-5-circumscribed-quadrilateral-tangent-pitot-ipad-1.jpg) |
Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1470](../school-college/5/p1470-tangential-quadrilateral-circle-rhombus-geogebra-1.jpg) |
Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent,
Parallel, Rhombus, Step-by-step Illustration. |
![Geometry Problem 1467](../school-college/5/p1467-square-rectangle-equal-area-geogebra-ipad-1.jpg) |
Geometry Problem 1467.
Square, Rectangle, Triangle, Area. |
![Geometry Problem 1466](../school-college/5/p1466-tangential-quadrilateral-newton-line-incenter-geogebra-ipad-1.jpg) |
Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1465](../school-college/5/p1465-tangential-quadrilateral-incenter-equal-sum-area-1.jpg) |
Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1464](../school-college/5/p1464-quadrilateral-midpoint-equal-sum-area-1.jpg) |
Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1463](../school-college/5/p1463-parallelogram-equal-sum-area-triangles-geogebra-1.jpg) |
Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1461](../school-college/5/p1462-newton-theorem-gauss-line-quadrilateral-midpoint-side-diagonal-geogebra-1.jpg) |
Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
![Geometry Problem 1461](../school-college/5/p1461-quadrilateral-angle-30-congruence-1.jpg) |
Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines. |
![Problem 1445](../school-college/5/p1445-van-aubel-theorem-quadrilateral-geogebra-step-1.jpg) |
Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra. |
![Problem 1435](../school-college/5/p1435-circle-diameter-tangent-parallelogram-1.jpg) |
Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points,
Poster, Typography, iPad Apps. |
![Problem 1428](../school-college/5/p1428-circle-tangent-triangle-square-area-1.jpg) |
Geometry Problem 1428. Intersecting Circles, Tangent Line, Triangle, Square, Area. |
![Problem 1426](../school-college/5/p1426-two-squares-triangle-quadrilateral-area-1.jpg) |
Geometry Problem 1426. Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas. |
![Problem 1424](../school-college/5/p1424-parallelogram-triangle-trapezoid-area-1.jpg) |
Geometry Problem 1424. Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement. |
![Problem 1422](../school-college/5/p1422-triangle-cevian-transversal-area-1.jpg) |
Geometry Problem 1422. Triangle, Transversal, Cevian, Area,
Quadrilateral, Measurement. |
![Problem 1403](../school-college/5/p1403-quadrilateral-congruence-90-degree-angle-tutor-1.jpg) |
Geometry Problem 1403. Quadrilateral, 90 Degree Angle, Perpendicular, Congruence. |
![Geometry problem 1356](../school-college/4/p1356-triangle-30-degrees-angle-congruence-tutoring-1.jpg) |
Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence. |
![Geometry problem 1334](../school-college/4/p1334-square-kite-sum-segment-1.jpg) |
Problem 1334. Square, Kite, Sum of Segments.
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![Geometry problem 1324](../school-college/4/p1324-quadrilateral-isosceles-45-degree-angle-1.jpg) |
Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence. |
![Geometry problem 1308](../school-college/4/p1308-quadrilateral-diagonal-incircle-tangent-1.jpg) |
Geometry Problem 1308.
Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement. |
![Geometry problem 1286](../school-college/3/p1286-quadrilateral-60-135-105-degrees-measurement-1.jpg) |
Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement. |
![Geometry problem 1285](../school-college/3/p1285-quadrilateral-60-150-90-degrees-measurement-1.jpg) |
Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement. |
![Geometry problem 1280](../school-college/3/p1280-quadrilateral-perpendicular-diagonal-collinear-tutoring-1.jpg) |
Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points. |
![Geometry problem 1267](../school-college/3/p1267-triangle-incircle-excircle-90-degree-parallelogram-1.jpg) |
Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram. |
![Geometry problem 1256](../school-college/3/p1256-parallelogram-angle-bisector-triangle-1.jpg) |
Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement. |
![Geometry problem 1243](../school-college/3/p1243-quadrilateral-angle-bisector-diagonal-1.jpg) |
Geometry Problem 1243.
Quadrilateral, Four Exterior Angle Bisectors, Semi-sum, Angles. Mobile Apps. |
![Geometry problem 1242](../school-college/3/p1242-quadrilateral-angle-bisector-collinearity-1.jpg) |
Geometry Problem 1242.
Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps. |
![Geometry problem 1241](../school-college/3/p1241-quadrilateral-exterior-angle-bisector-circle-cyclic-1.jpg) |
Geometry Problem 1241.
Quadrilateral, Four Exterior Angle Bisectors, Cyclic Quadrilateral, Circle. Mobile Apps. |
![Geometry problem 1234](../school-college/3/p1234-quadrilateral-60-degrees-cyclic-concyclic-midpoint-1.jpg) |
Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points. |
![Geometry problem 1230](../school-college/3/p1230-quadrilateral-equilateral-triangle-metric-relations-1.jpg) |
Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations. |
![Geometry problem 1226](../school-college/3/p1226-quadrilateral-midpoint-square-class-1.jpg) |
Geometry Problem 1226
Quadrilateral, Squares, Centers, Midpoints, Congruence. |
![Geometry problem 1203](../school-college/3/p1203-right-triangle-angle-bisector-quadrilateral-congruence-1.jpg) |
Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals. |
![Geometry problem 1198](../school-college/2/p1198-right-triangle-square-rectangle-quadrilateral-area-1.jpg) |
Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas. |
![Geometry problem 1192](../school-college/2/p1192-trapezoid-triangle-midpoint-area-1.jpg) |
Geometry Problem 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel. |
![Geometry problem 1188](../school-college/2/p1188-triangle-parallelogram-area-trapezoid-congruence-parallel-1.jpg) |
Geometry Problem 1188
Triangle, Parallelogram, Parallel Lines, Trapezoid, Area. |
![Geometry problem 1187](../school-college/2/p1187-triangle-quadrilateral-hexagon-midpoint-area-1.jpg) |
Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area. |
![Geometry problem 1186](../school-college/2/p1186-right-triangle-square-circle-tangent-area-1.jpg) |
Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area. |
![Geometry problem 1185](../school-college/2/p1185-two-similar-rectangles-sum-areas-metric-relations-1.jpg) |
Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations. |
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