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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Four lines intersect,
Sides, angles, shapes perplex,
Quadrilateral quests. |
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Parallelograms Index.
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Word Cloud of Quadrilateral.
Visual Summary. |
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Square. |
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Area of a Square Index.
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Rectangle. Theorems and Problems Index. |
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Rhombus.
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Trapezoids.
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Median of a Trapezoid, Theorems and Problems.
Index.
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Cyclic Quadrilateral.
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Tangential or Circumscribed Quadrilateral
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Kite Index.
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Complete Quadrilateral Index.
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Equilic Quadrilateral.
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Triangle and Squares. 21 theorems. Visual
illustrations. |
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van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation for Tablets, iPad,
Nexus, Galaxy. |
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Golden Rectangles. |
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Ptolemy's Theorem.
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Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem. |
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Tangential or Circumscribed Quadrilateral: Pitot Theorem. |
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Geometry Problem 1583:
Prove Lines CK and BL are Parallel. |
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Geometry Problem 1581:
Prove the Angle Bisection in a Cyclic Quadrilateral. |
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Geometry Problem 1582:
Prove That Angles AFD and AEF Are Equal in This Secant Problem. |
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Geometry Problem 1578:
Find the Area of a Bicentric Quadrilateral with Perpendicular Extensions of Opposite Sides!. |
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Geometry Problem 1570:
Calculating BE in Overlapping Squares: A High School and College Geometry Challenge. |
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Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. |
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Geometry Problem 1568:
Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle. |
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Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. |
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Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
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Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. |
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Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. |
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Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
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Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
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Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
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Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. |
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Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
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Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. |
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Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent,
Parallel, Rhombus, Step-by-step Illustration. |
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Geometry Problem 1467.
Square, Rectangle, Triangle, Area. |
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Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
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Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines. |
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Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra. |
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Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points,
Poster, Typography, iPad Apps. |
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Geometry Problem 1428.
Intersecting Circles, Tangent Line, Triangle, Square, Area. |
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Geometry Problem 1426.
Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas. |
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Geometry Problem 1424.
Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement. |
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Geometry Problem 1422.
Triangle, Transversal, Cevian, Area,
Quadrilateral, Measurement. |
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Geometry Problem 1403.
Quadrilateral, 90 Degree Angle, Perpendicular, Congruence. |
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Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence. |
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Problem 1334. Square, Kite, Sum of Segments.
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Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence. |
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Geometry Problem 1308.
Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement. |
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Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement. |
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Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement. |
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Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points. |
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Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram. |
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Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement. |
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Geometry Problem 1243.
Quadrilateral, Four Exterior Angle Bisectors, Semi-sum, Angles. Mobile Apps. |
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Geometry Problem 1242.
Quadrilateral, Four Interior and Exterior Angle Bisectors, Collinearity, Concurrent Lines. Mobile Apps. |
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Geometry Problem 1241.
Quadrilateral, Four Exterior Angle Bisectors, Cyclic Quadrilateral, Circle. Mobile Apps. |
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Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points. |
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Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations. |
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Geometry Problem 1226
Quadrilateral, Squares, Centers, Midpoints, Congruence. |
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Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals. |
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Geometry Problem 1198
Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas. |
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Geometry Problem 1192
Trapezoid, Triangle, Diagonal, Midpoint, Area, Parallel. |
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Geometry Problem 1188
Triangle, Parallelogram, Parallel Lines, Trapezoid, Area. |
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Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area. |
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Geometry Problem 1186
Right Triangle, Square, Inscribed Circle, Tangent, Quadrilateral, Area. |
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Geometry Problem 1185
Similar Rectangles, Four Quadrilaterals, Sum of the Areas, Metric Relations. |
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