College Geometry Online, eLearning


Online Geometry: Congruence, Rotation, Translation, Reflection - Page 1

Congruence, Translation, Rotation, Reflection


Euclid's Elements 23 definitions

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Perpendicular Bisector Index

Perpendicular Bisector.

Kaleidoscope Index

Kaleidoscope Index.

Reflection Index

Reflection, Theorems and Problems.


Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS)

iPad Geoboard: Pythagorean Theorem proof by Leonardo 

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

iPad Geoboard: Pythagorean Theorem proof 

Geoboard for iPad Pythagorean Theorem Proof, Squares (Problem 540).

iPadd Apps Geoboard, triangle with two squares

Geoboard for iPad Gallery: Triangle with two squares (Problem 496).

Semiperimeter and excircles of a triangle.


Semiperimeter and incircle of a triangle.

Semiperimeter, incircle and excircles of a triangle.


Parallelogram with Squares theorem Thébault's Theorem.

Johnson: Intersecting circles

Johnson's Theorem, Intersecting circles.
HTML5 Animation

Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and trisection points of the edges.


Van Aubel

Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.

Langley's Problem Adventitious angles. 20° isosceles triangle with animation.

Geometry Problem 1560

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

Geometry Problem 1559

Geometry Problem 1559: Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels.

Geometry Problem 1558

Geometry Problem 1558: The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle.

Geometry Problem 1557

Geometry Problem 1557: Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral, isosceles, midpoint and congruence

Geometry Problem 1556

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence

Geometry Problem 1554

Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC

Geometry Problem 1553

Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors

Geometry Problem 1550

Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation

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 1529

Geometry Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge.

Geometry Problem 1526

Geometry Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.

Geometry Problem 1525

Geometry Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments.

Geometry Problem 1524

Geometry Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors.

Geometry Problem 1523

Geometry Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle - Get Expert Geometry Tips Now! .

Geometry Problem 1513

Geometry Problem 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two Sides. Difficulty Level: High School.

Geometry Problem 1511

Geometry Problem 1511 and Poem.
Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School.

Geometry Problem 1510

Geometry Problem 1510 and Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School.

Geometry Problem 1509

Geometry Problem 1509 and Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School.

Geometry Problem 1503

Geometry Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular.

Geometry Problem 1501

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

Geometry Problem 1498

Geometry Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction.

Geometry Problem 1496

Geometry Problem 1496.
Triangle, Congruence, Isosceles, Double Angle, 30 Degrees.

Geometry Problem 1461

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

Problem 1447

Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step illustration using GeoGebra.

Problem 1445

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

Problem 1431

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Problem 1429

Geometry Problem 1429.
Triangle, Median, 15-30 degree, Angle, Congruence.

Problem 1428

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

Problem 1406

Geometry Problem 1406.
Four Congruent Circles, Measurement, Metric Relations, Sum of the Squares.

Problem 1405

Geometry Problem 1405.
Four Congruent Circles, Congruent Chords.

Problem 1404

Geometry Problem 1404.
Three Circles, Center, Intersecting Points, Collinearity, Congruence.

Problem 1403

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

Problem 1401

Geometry Problem 1401.
Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence.

Problem 1389 40-120-20 triangle

Geometry Problem 1389.
Triangle, 40-120-20 degree, Angle, Congruence.

Problem 1388 40-60-80 triangle

Geometry Problem 1388.
Triangle 40-60-80 degree, Incenter, Congruence.

Problem 1382 Circle, Diameter, Radius, Perpendicular, Congruence

Geometry Problem 1382.
Circle, Diameter, Radius, Perpendicular, Congruence.

Problem 1380 Circles, Tangents, Chords

Geometry Problem 1380.
Common Internal Tangents. Circles, Secant, Congruent Chords.

Problem 1379 Circles, Tangents, Chords

Geometry Problem 1379.
Common External Tangents. Circles, Secant, Congruent Chords.

Geometry problem 1361

Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Geometry problem 1359

Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints.

Geometry problem 1356

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

Geometry problem 1353

Geometry Problem 1353.
Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees.

Geometry problem 1349

Geometry Problem 1349.
Three Squares, 90 Degrees, Perpendicular Lines, Diagonal. Math Infographic.

Geometry problem 1348

Geometry Problem 1348.
Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence.

Geometry problem 1347

Geometry Problem 1347.
Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle.

Geometry problem 1329

Geometry Problem 1329.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Congruence.

Geometry problem 1328

Geometry Problem 1328.
Two Squares Side by Side, Perpendicular, 90 Degrees, Congruence.

Geometry problem 1317

Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence.

Geometry problem 1316

Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence.

Geometry problem 1315

Geometry Problem 1315.
Triangle, Incircle, Tangent, Chord, Circle, Congruence.

Geometry problem 1314

Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence.

Geometry problem 1313

Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence.

Geometry problem 1304

Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement.

Geometry problem 1303

Geometry Problem 1303.
Triangle, 60 Degrees, Angle Bisector, Measurement.

Geometry problem 1302

Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence.

Geometry problem 1295

Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle.

Geometry problem 1293

Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint.

Geometry problem 1291

Geometry Problem 1291.
Three Squares, Collinear Vertices, Midpoint, Congruence.

Geometry problem 1287

Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, 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 1284

Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence.

Geometry problem 1278

Geometry Problem 1278.
Square, 3-4-5 Right Triangle, Midpoint.

Geometry problem 1272

Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence.

Geometry problem 1250

Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence.

Geometry problem 1238

Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps.

Geometry problem 1237

Geometry Problem 1237
IMO 2016, Problem 1, Triangle, Congruence, Parallel Lines, Midpoint, Concurrency.

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HomeGeometry | Congruence | Email | by Antonio Gutierrez
Last updated: Dec 14, 2023