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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.


Quadrilateral Index

Four lines intersect,
Sides, angles, shapes perplex,
Quadrilateral quests.

Parallelograms Index

Parallelograms Index.

Quadrilateral Word Cloud

Word Cloud of Quadrilateral.
Visual Summary.

Squares Index


Area of a square

Area of a Square Index.

Rectangle Index

Rectangle. Theorems and Problems Index.

Rhombus, Rhombuses, Rhombi


Trapezoid Index


Trapezoid median, Theorems and Problems, Index

Median of a Trapezoid, Theorems and Problems. Index.

Cyclic Quadrilateral Index

Cyclic Quadrilateral.

Tangential or Circumscribed Quadrilateral Index, theorems and problems

Tangential or Circumscribed Quadrilateral

Kite Index

Kite Index.

Complete quadrilateral

Complete Quadrilateral Index.

Equilic Quadrilateral

Equilic Quadrilateral.

Triangle and Squares. 21 theorems. Visual illustrations.

van Aubel theorem for Tablets, iPad, Nexus, Galaxy

van Aubel's Theorem. Quadrilateral with Squares. Proof with animation for Tablets, iPad, Nexus, Galaxy.

Golden Rectangles Index

Golden Rectangles.

Ptolemy's Theorem.

Tangential Quadrilateral

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Tangential Quadrilateral: Pitot Theorem

Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Geometry Problem 1564

Geometry Problem 1564: Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.

Geometry Problem 1560

Geometry Problem 1560: Trapezoid ABCD: Unlocking Angle Secrets at G and H.

Geometry Problem 1543

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

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

Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?.

Geometry Problem 1536

Geometry Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals.

Geometry Problem 1508

Geometry Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School.

Geometry Problem 1502

Geometry Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral.

Geometry Problem 1501

Geometry Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement.

Dynamic Geometry 1481

Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1470

Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration.

Geometry Problem 1467

Geometry Problem 1467.
Square, Rectangle, Triangle, Area.

Geometry Problem 1466

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1465

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1464

Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1463

Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas. Step-by-step Illustration using GeoGebra.

Geometry Problem 1461

Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals, Collinear Points.

Geometry Problem 1461

Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines.

Problem 1445

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra.

Problem 1435

Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points, Poster, Typography, iPad Apps.

Problem 1428

Geometry Problem 1428.
Intersecting Circles, Tangent Line, Triangle, Square, Area.

Problem 1426

Geometry Problem 1426.
Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas.

Problem 1424

Geometry Problem 1424.
Triangle, Parallelogram, Trapezoid, Area, Diagonal, Measurement.

Problem 1422

Geometry Problem 1422.
Triangle, Transversal, Cevian, Area, Quadrilateral, Measurement.

Problem 1403

Geometry Problem 1403.
Quadrilateral, 90 Degree Angle, Perpendicular, Congruence.

Geometry problem 1356

Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence.

Geometry problem 1334

Problem 1334. Square, Kite, Sum of Segments.

Geometry problem 1324

Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence.

Geometry problem 1308

Geometry Problem 1308.
Quadrilateral, Diagonal, Triangle, Incircle, Tangent Line, Sides, Measurement.

Geometry problem 1286

Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement.

Geometry problem 1285

Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement.

Geometry problem 1280

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

Geometry problem 1267

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

Geometry problem 1256

Geometry Problem 1256.
Parallelogram, Angle Bisector, Measurement.

Geometry problem 1243

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

Geometry problem 1242

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

Geometry problem 1241

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

Geometry problem 1234

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

Geometry problem 1230

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

Geometry problem 1226

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

Geometry problem 1203

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

Geometry problem 1198

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

Geometry problem 1192

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

Geometry problem 1188

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

Geometry problem 1187

Geometry Problem 1187
Triangle, Quadrilateral, Midpoints, Area.

Geometry problem 1186

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

Geometry problem 1185

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

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Last updated: Jul 17, 2024