

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. 

Median
length, Apollonius' Theorem 

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. 

NinePoint Center, NinePoint Circle, Euler Line.
Interactive illustration.
Median.


Heron's Formula with medians.
Medians. 

Newton's Theorem,
NewtonGauss Line: Complete quadrilateral theorem. Using TracenPoche
Dynamic Geometry Software, Online
StepbyStep construction, manipulation, and animation.
Medians. 

Feuerbach Points and NinePoint Circle with interactive
animation, manipulation, and stepbystep construction. 

Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. 

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

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 151a>.
Quadrilateral, Area, Trisection of Sides.
Midpoints. 

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.


Proposed Problem 146>. V. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. 

Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
StepbyStep 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.


Proposed Problem 46.
Angles and triangles. Midpoints.







