Mastering Medians and Triangles in Geometry: The Ultimate Collection of Theorems and Problems on gogeometry.com

This website provides a collection of problems and theorems related to medians and triangles in geometry. Some of the topics covered include the properties of medians, centroids, inequalities involving medians, and the relationship between medians and other elements of a triangle.

The website offers a variety of problems with detailed solutions, as well as interactive applets and videos to help students better understand the concepts. The problems range in difficulty from basic to advanced, making it a useful resource for both beginners and advanced learners of geometry.

Overall, this website is a great tool for anyone looking to improve their understanding of medians and triangles in geometry, and is particularly useful for students preparing for geometry competitions or exams.

Median of a Triangle - Table of Content

Points, Theorems and Problems - Index.
Intersection Point.

Centroid /Barycenter. Index.
Medians.

GeoGebra, Dynamic Geometry: Centroid of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Symmedian (Lemoine) Point
Symmedian is the line symmetric of the median with respect to the bisector of the angle from which the median is drawn.

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

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

Heron's Formula with medians.
Medians
.

Newton's Theorem, Newton-Gauss Line: Complete quadrilateral theorem. Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation. Medians.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

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

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

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 1383.
Triangle, Median, Circle, Chord, Secant, Sum, Product.

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

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

Geometry Problem 1290.
Triangle, Internal Angle Bisector, Median, Parallel, Measurement, Metric Relations.

Geometry Problem 1273.
Circle, Tangent, Secant, Midpoint, Isogonal Lines, Congruent Angles.

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

Geometry Problem 1263.
Triangle, Medians, 90 Degrees, Perpendicular.

Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular.

Geometry Problem 1128.
Right Triangles, Medians, Parallel, Angles, Congruence, Half the measure.

Geometry Problem 1125.
Triangle, Four Equilateral Triangles, Centroid, Midpoint.

Geometry Problem 1124.
Triangle, Median, Two Squares, Area.

Geometry Problem 1053.
Triangle, Two Perpendicular Medians, Midpoint, Congruence.

Geometry Problem 1007.
Hexagon, Midpoint, Triangle, Median, Centroid, Concurrency.

Geometry Problem 999.
Right Triangle, Midpoint, Median, Double Angle, Congruence.

Geometry Problem 990.
Triangle, Incircle, Median, Cevian, Central Angle, Congruence, Circle, Secant, Midpoint, Parallel.

Geometry Problem 986.
Triangle, Median, Midpoint, Equal Angles, 45 Degrees.

Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.

Geometry Problem 896
Triangle, Orthocenter, Midpoint, Median, Intersecting Circles, Diameter, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint.

Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence.

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines.

Geometry Problem 802
Scalene Triangle, Median, Perpendicular, Angle, Measurement.

Geometry Problem 734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence, Midpoint.

Geometry Problem 714.
Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem.

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Problem 528.
Triangle, Medians, Perpendicular, Measurement.

Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.

Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Median.

Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Median.

Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.
Midpoints.

Proposed Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.
Median.

Proposed Problem 176. Quadrilateral with Midpoints, Triangles, Median, Areas.

Proposed Problem 175. Quadrilateral with Midpoints, Areas.

Proposed Problem 174. Quadrilateral with Midpoints, Triangles, Median, Areas.

Proposed Problem 173. Quadrilateral with Midpoints, Triangles, Median, Areas.

Proposed Problem 172. Trapezoid, Midpoints, Quadrilaterals, Areas.

Proposed Problem 171. Trapezoid, Midpoints, Triangles, Median, Areas.

Proposed Problem 170. Trapezoid, Midpoint, Triangle, Median, Area.

Proposed Problem 161. Parallelogram, Midpoints, Octagon, Median, Areas.

Proposed Problem 150. Quadrilateral, Area, Trisection of Sides.
Midpoints.

PrProposed Problem 149. Quadrilateral, Median, Area, Midpoints.

Proposed Problem 148. Quadrilateral, Median, Area, Midpoints.

Proposed Problem 147. Quadrilateral, Median, Area, Midpoints, Triangle.

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Median.

Proposed Problem 108. Angles, Triangle, Median. Median.

Proposed Problem 98. Quadrilateral Area, Centroid, Similarity, Midpoints.

ProProposed Problem 90. Quadrilateral and Triangle Areas, Midpoints, Median.

Proposed Problem 89. Triangles of equal area, Midpoints, Median.

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints, Median.

Proposed Problem 87. Area of Quadrilaterals and Midpoints of Diagonals, Median.

Proposed Problem 1: Angles of a Triangle. Median, Congruence. Hints are provided.

Proposed Problem 47. Angles and triangles.
Median.

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