College Geometry Online, eLearning

Math: Geometry: Midpoint, Theorems and Problems

Midpoint's perfect line,
Theorems and problems align,
Geometry divine.

Midpoint Index


Point, Theorems and Problems, Index

Points, Theorems and Problems - Index.

Perpendicular Bisector Index

Perpendicular Bisector.

Butterfly Theorem Proof with animation.
Midpoint of a chord.

Trapezoid median, Theorems and Problems, Index

Median of a Trapezoid, Theorems and Problems. Index.

Newton's Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of diagonals, center of the circle inscribed.

Dynamic Geometry: Nine Point Circle. HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..)

Dynamic Geometry: Internal Feuerbach Point. HTML5 Animation for Tablets iPad, Nexus

GeoGebra, Dynamic Geometry: Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..)

Equilic Quadrilateral.
120 degrees.

Kurschak's Tile and Theorem. Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric way of finding the area of a regular dodecagon.

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


Median Length theorem

Median length, Apollonius' Theorem

Van Aubel

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

Symmedian (Lemoine) Point
Triangle Center

Archimedes' Book of Lemmas: Proposition 7
Square and inscribed and circumscribed Circles

Archimedes' Book of Lemmas: Proposition 2
Semicircle, diameter, tangents, secant line. 

Archimedes' Book of Lemmas: Proposition 3
Semicircle, perpendicular to diameter, chords.

Archimedes' Book of Lemmas: Proposition 10
Tangents to a circle, secant line and chords, Parallel.

Archimedes' Book of Lemmas: Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Midpoint, Perpendicular, Radius

Bottema Theorem. Elearning.

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Eight Point Circle Theorem. Elearning

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
Perpendiculars from the midpoints.

Marion Walter's Theorem: Triangle and Hexagon areas: Using TracenPoche Dynamic Geometry Software.

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.

Mascheroni Construction with compass alone. Midpoint of a segment.

Heron's Formula with medians.

Mittenpunkt Point

Brahmagupta's Theorem

Dynamic Geometry: Brahmagupta Theorem, . GeoGebra, HTML5 Animation for Tablets

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 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 1548

Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes

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 1539

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!.

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 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 1522

Geometry Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths.

Geometry Problem 1519

Geometry Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines.

Geometry Problem 1517

Geometry Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School.

Geometry Problem 1515

Geometry Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School.

Geometry Problem 1512

Geometry Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School.

Geometry Problem 1494

Geometry Problem 1494.
Parallelogram, Midpoints, Octagon, Areas.

Dynamic Geometry 1476

Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1474

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration.

Dynamic Geometry 1469

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration.

Geometry Problem 1466

Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. 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 1461

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

Geometry Problem 1460

Dynamic Geometry 1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals, Collinear Points, Step-by-step Illustration using GeoGebra.

Geometry Problem 1459

Geometry Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra.

Problem 1444

Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra.

Problem 1429

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

Problem 1417

Geometry Problem 1417.
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector, Tangent Lines, Tangent Circles, Midpoint.

Problem 1408

Geometry Problem 1408.
Right Triangle, Incircle, Excircle, Incenter, Midpoint, Tangency Point, Collinearity.

Problem 1395

Geometry Problem 1395.
Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency.

Problem 1388 Circle, Triangle

Geometry Problem 1385.
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points.

Geometry problem 1365

Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps.

Geometry problem 1360

Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps.

Geometry problem 1359

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

Geometry problem 1355

Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments.

Geometry problem 1351

Geometry Problem 1351.
Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars.

Geometry problem 1342

Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.

Geometry problem 1336

Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.

Geometry problem 1325

Geometry Problem 1325.
Octagons, Midpoints, Squares, Mobile Apps, iPad.

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 1302

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

Geometry problem 1301

Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency.

Geometry problem 1298

Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint.

Geometry problem 1294

Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points.

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.

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Last updated: Dec 14, 2023