![](../landscape/landscape_px1.gif) |
|
![College Geometry Online, eLearning](../machu_picchu_h1_910.jpg)
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
|
![Point, Theorems and Problems, Index](point_theorems_index_17.jpg) |
Points, Theorems and Problems - Index.
Intersection Point. |
![Median Length theorem](median_length_17.jpg) |
Median
length, Apollonius' Theorem |
![Centroid of a triangle Index](../center/centroid_barycenter_index.jpg) |
Centroid /Barycenter. Index.
Medians.
|
![Dynamic Geometry: Centroid of a Triangle. HTML5 Animation for Tablets (iPad, Nexus..)](../geogebra/geogebra-triangle-centroid-median-html5-animation-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry:
Centroid
of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..) |
![](../center/lemoine_point_170.jpg) |
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_theorem.jpg) |
Marion
Walter's Theorem: Triangle and Hexagon areas:
Using TracenPoche Dynamic Geometry Software.
Medians. |
![](../center/nine_point_center_euler_170.jpg) |
Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
Median.
|
![](../heron/heron_medians_170x100.jpg) |
Heron's Formula with medians.
Medians. |
![](newton_theorem_line_17.jpg) |
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_17.jpg) |
Feuerbach Points and Nine-Point Circle with interactive
animation, manipulation, and step-by-step construction. |
![Geometry Problem 1565](../school-college/6/p1565-triangle-median-perpendicular-midpoint-congruence-tutoring-1.jpg) |
Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. |
![Geometry Problem 1554](../school-college/6/p1554-triangle-ABC-angles-A-B-altitude-AH-median-AM-length-HM-4-units-length-AB-1.jpg) |
Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC |
![Geometry Problem 1522](../school-college/6/p1522-triangle-median-double-angle-side-geometry-poem-1.jpg) |
Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. |
![Geometry Problem 1517](../school-college/6/p1517-unlock-triangle-side-length-solving-median-angles-1.jpg) |
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](../school-college/6/p1512-triangle-median-cevian-given-ratio-midpoint-midline-theorem-poem-1.jpg) |
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. |
![Problem 1383 Circle, Triangle](../school-college/4/p1383-triangle-circle-midpoint-sum-product-secant-1.jpg) |
Geometry Problem 1383. Triangle, Median, Circle, Chord, Secant, Sum, Product. |
![Geometry problem 1355](../school-college/4/p1355-triangle-median-circle-measurement-tutoring-1.jpg) |
Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments. |
![Geometry problem 1302](../school-college/4/p1302-triangle-median-circle-congruence-1.jpg) |
Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. |
![Geometry problem 1290](../school-college/3/p1290-triangle-median-angle-bisector-parallel-1.jpg) |
Geometry Problem 1290.
Triangle, Internal Angle Bisector, Median, Parallel, Measurement, Metric Relations. |
![Geometry problem 1273](../school-college/3/p1273-triangle-circle-tangent-midpoint-equal-angle-tutoring-1.jpg) |
Geometry Problem 1273.
Circle, Tangent, Secant, Midpoint, Isogonal Lines, Congruent Angles. |
![Geometry problem 1272](../school-college/3/p1272-isosceles-triangle-altitude-midpoint-angle-1.jpg) |
Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence. |
![Geometry problem 1263](../school-college/3/p1263-triangle-medians-90-degree-perpendicular-1.jpg) |
Geometry Problem 1263.
Triangle, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1262](../school-college/3/p1262-isosceles-triangle-altitude-median-90-degree-1.jpg) |
Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1128](../school-college/2/p1128-right-triangle-median-parallel-angle-hypotenuse-1.jpg) |
Geometry Problem 1128.
Right Triangles, Medians, Parallel, Angles, Congruence, Half the measure. |
![Geometry problem 1125](../school-college/2/p1125-triangle-four-equilateral-centroid-midpoint-1.jpg) |
Geometry Problem 1125.
Triangle, Four Equilateral Triangles, Centroid, Midpoint. |
![Geometry problem 1124](../school-college/2/p1124-triangle-median-square-area-math-1.jpg) |
Geometry Problem 1124.
Triangle, Median, Two Squares, Area. |
![Geometry Problem 1053](../school-college/1/p1053-perpendicular-medians-triangle-congruence-math-1.jpg) |
Geometry Problem
1053.
Triangle, Two Perpendicular Medians, Midpoint, Congruence. |
![Geometry Problem 1007](../school-college/1/p1007-hexagon-midpoint-triangle-median-centroid-concurrent-math-1.jpg) |
Geometry Problem
1007.
Hexagon, Midpoint, Triangle, Median, Centroid, Concurrency. |
![Geometry Problem 999](../school-college/p999-right-triangle-double-angle-congruence-math-1.jpg) |
Geometry Problem 999.
Right Triangle, Midpoint, Median, Double Angle, Congruence. |
![Geometry Problem 990](../school-college/p990-triangle-incircle-median-circle-central-angle-congruence-1.jpg) |
Geometry Problem 990.
Triangle, Incircle, Median, Cevian, Central Angle, Congruence, Circle, Secant, Midpoint,
Parallel. |
![Geometry Problem 986](../school-college/p986-triangle-median-45-degrees-angle-1.jpg) |
Geometry Problem 986.
Triangle, Median, Midpoint, Equal Angles, 45 Degrees. |
![Problem 928](../school-college/p928-triangle-area-median-cevian-concurrency-1.jpg) |
Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.
|
![Geometry Problem 896](../school-college/p896-triangle-orthocenter-midpoint-circle-diameter-collinear-html5-ipad-1.jpg) |
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](../school-college/p870-triangle-median-three-square-collinear-midpoint-1.jpg) |
Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint. |
![Geometry problem 867, Isosceles Triangle, Median, Perpendicular, Angle, Congruence](../school-college/p867-triangle-isosceles-angles-congruence-1.jpg) |
Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence. |
![Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence](../school-college/p860-triangle-three-medians-area-1.jpg) |
Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence. |
![Problem 856: Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines](../school-college/p857-triangle-median-midpoint-angle-30-degrees-1.jpg) |
Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines. |
![Scalene Triangle, Median, Perpendicular, Angle, Measurement](../school-college/p802-triangle-median-perpendicular-angle-1.jpg) |
Geometry Problem
802
Scalene Triangle, Median, Perpendicular, Angle, Measurement. |
![Triangle, Median, Isosceles, Congruence, Parallel](../problem/p734_triangle_median_1.jpg) |
Geometry Problem
734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence, Midpoint. |
![Triangle, Parallel, Concurrent, Ceva, Midpoint](../problem/p714_triangle_parallel_1.jpg) |
Geometry Problem
714.
Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem. |
![Triangle, Circle, Median, Proportion](../problem/p679-triangle-circle-1.jpg) |
Geometry Problem 679.
Triangle, Circle, Median, Proportion. |
![Online Math: Geometry Problem 572, Right triangle and Circle](../problem/p572_right_triangle_circle1.jpg) |
Problem
572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles. |
![Triangle, Medians, Perpendicular](../problem/p528_triangle_medians_1.jpg) |
Problem 528.
Triangle, Medians, Perpendicular, Measurement. |
![Hexagon, Centroids](../problem/p402_hexagon_centroid_17.jpg) |
Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity. |
![Problem 263: Triangle, Median Projection](../problem/p263_triangle_median_17.jpg) |
Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides. |
![Problem 254: Triangle and Centroid](../problem/p255_triangle_centroid_17.jpg) |
Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Median. |
![Elearning 254: Triangle and Centroid](../problem/p254_triangle_centroid_17.jpg) |
Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
Median. |
![Elearning 253: Triangle, Centroid](../problem/p253_triangle_centroid_17.jpg) |
Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.
Midpoints. |
![Quadrilateral, diagonals, midpoints](../problem/p250_quadrilateral_17.jpg) |
Proposed Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.
Median.
|
![Elearning 176: Quadrilateral Area Problem](../problem/p176_quadrilateral_area_17.jpg) |
Proposed Problem 176.
Quadrilateral with Midpoints, Triangles, Median, Areas.
|
![Elearning 175: Quadrilateral Area Problem](../problem/p175_quadrilateral_area_17.jpg) |
Proposed Problem 175.
Quadrilateral with Midpoints, Areas.
|
![Quadrilateral with Midpoints, Triangles Area](../problem/p174_quadrilateral_area_17.jpg) |
Proposed Problem 174.
Quadrilateral with Midpoints, Triangles, Median, Areas.
|
![Quadrilateral with Midpoints, Triangles Area](../problem/p173_quadrilateral_area_17.jpg) |
Proposed Problem 173.
Quadrilateral with Midpoints, Triangles, Median, Areas.
|
![Elearning 172: Trapezoid, Quadrilateral, Area](../problem/p172_trapezoid_quadrilatera.jpg) |
Proposed Problem 172. Trapezoid,
Midpoints, Quadrilaterals, Areas.
|
![Elearning 172: Trapezoid, Midpoints, Quadrilaterals, Areas](../problem/p171_trapezoid_triangle_17.jpg) |
Proposed Problem 171. Trapezoid,
Midpoints, Triangles,
Median, Areas.
|
![Trapezoid, Triangle, Area](../problem/p170_trapezoid_triangle_17.jpg) |
Proposed Problem 170. Trapezoid,
Midpoint, Triangle,
Median, Area.
|
![Elearning 161 Parallelogram and Octagon Areas](../problem/p161_parallelogram_area_17.jpg) |
Proposed Problem 161.
Parallelogram, Midpoints, Octagon,
Median, Areas.
|
![Quadrilateral area, trisection](../problem/p151_quadrilateral_area_17.jpg) |
Proposed Problem 151a>.
Quadrilateral, Area, Trisection of Sides.
Midpoints. |
![Quadrilateral area, trisection](../problem/p150_quadrilateral_area_17.jpg) |
Proposed Problem 150.
Quadrilateral, Area, Trisection of Sides.
Midpoints. |
![Quadrilateral Area, Midpoint, Elearning](../problem/p149_quadrilateral_area_17.jpg) |
PrProposed Problem 149.
Quadrilateral,
Median, Area, Midpoints.
|
![Quadrilateral area, Midpoint, Elearning](../problem/p148_quadrilateral_area_17.jpg) |
Proposed Problem 148.
Quadrilateral,
Median, Area, Midpoints.
|
![Quadrilateral Area, Elearning](../problem/p147_quadrilateral_area_17.jpg) |
Proposed Problem 147.
Quadrilateral,
Median, Area, Midpoints, Triangle.
|
![Quadrilateral Area, Midpoint](../problem/p146_quadrilateral_area_17.jpg) |
Proposed Problem 146>. V. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. |
![Trapezoid](trapezoid_diagonal_01_17.jpg) |
Trapezoid,
Triangle, Diagonals, Midpoints.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Median. |
![Problem 108. Elearning.](../problem/p108_angle_triangle_median_17.jpg) |
Proposed Problem 108. Angles,
Triangle, Median.
Median. |
![Quadrilateral Area, Elearning.](../problem/p098_quadrilateral_area_17.jpg) |
Proposed Problem 98. Quadrilateral Area, Centroid, Similarity, Midpoints. |
![Geometry problem](../problem/p090_quadrilateral_area_17.jpg) |
ProProposed Problem 90.
Quadrilateral and Triangle Areas, Midpoints,
Median. |
![Math problem](../problem/p089_equal_area_17.jpg) |
Proposed Problem 89. Triangles of equal area, Midpoints, Median. |
![Math problem](../problem/p088_quadrilateral_area_17.jpg) |
Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints,
Median. |
![Quadrilateral area problem](../problem/p087_quadrilateral_area_17.jpg) |
Proposed Problem 87. Area of
Quadrilaterals and Midpoints of Diagonals,
Median. |
![](../problem/problem001_angle_triangle_1.jpg) |
Proposed Problem 1:
Angles of a Triangle.
Median, Congruence. Hints are
provided. |
![](../problem/p047_angle_triangle_170.jpg) |
Proposed Problem 47.
Angles and triangles.
Median.
|
![](../problem/p046_angle_triangle_170.jpg) |
Proposed Problem 46.
Angles and triangles. Midpoints.
|
|
|
|
|
|
![](../landscape/landscape_bg_right.gif) |
![](../landscape/landscape_px1.gif) |