A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side. Every triangle has three medians, and they always meet at one point, the centroid. The centroid divides each median in a 2 : 1 ratio, with the longer part next to the vertex.
In Spanish
mediana de un triángulo
Also called
triangle median, median (geometry)
Grade level
Geometry
GeometryCCSS HSG-CO.C.10SATACT
Median of a Triangle in a picture
Each median ends at the midpoint of a side. All three cross at the centroid, which sits two thirds of the way down each median.
Formal definition and notation
In triangleABC, the median from A is the segment AM, where M is the midpoint of BC. The three medians are concurrent at the centroid G, with AG = 23AM. For vertices (x1, y1), (x2, y2), (x3, y3), the centroid is ( x1 + x2 + x33, y1 + y2 + y33 ).
Symbol
Read it as
Meaning
AM
segment A M
the median from vertex A to the midpoint M of the opposite side
The median of a data set is its middle value when the data are sorted, such as 7 for 3, 7, 9. A median of a triangle is a segment.
Median of a Trianglevs.Altitude
An altitude goes from a vertex to the opposite side (or its extension) at a right angle. A median goes to the midpoint of that side.
Quick check: 3 questions
Question 1 of 3
A median of a triangle connects a vertex to what point?
Show answer and explanation
Answer: C. A median ends at the midpoint of the side opposite its vertex. Choice B describes an altitude, and D is the circumcenter.
Question 2 of 3
A median of a triangle is 27 cm long. How far is the centroid from the vertex on that median?
Show answer and explanation
Answer: C. The centroid is two thirds of the way from the vertex: 23 × 27 = 18. A assumes the halfway point, and B is the distance from the centroid to the midpoint.
Question 3 of 3
What is the centroid of the triangle with vertices (1, 2), (5, 8) and (9, −1)?
Show answer and explanation
Answer: A. Average each coordinate: 1 + 5 + 93 = 5 and 2 + 8 − 13 = 3. D forgets to divide, and B and C divide by 2 instead of 3.
Median of a Triangle: frequently asked questions
How many medians does a triangle have?
Three, one from each vertex to the midpoint of the side across from it. All three always pass through a single point, the centroid, no matter what shape the triangle is. Because the centroid is always inside the triangle, every median lies inside it too, even in an obtuse triangle.
What is the difference between a median and an altitude of a triangle?
Both start at a vertex. A median ends at the midpoint of the opposite side, cutting it into two equal pieces. An altitude meets the opposite side, or the line through it, at a right angle, and measures the height. They are the same segment only in special cases, such as the median to the base of an isosceles triangle.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS HSG-CO.C.10
Cite this entry
Effortless Math Team. “Median of a Triangle.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/median-of-a-triangle/
Flashcard
TermMedian of a Trianglevertex to opposite midpoint
DefinitionA segment from a vertex to the midpoint of the opposite side. The three medians meet at the centroid, which splits each one 2 : 1.
MidpointA midpoint is the point exactly halfway between the two endpoints of a line segment, so it splits the segment into two equal parts. On the coordinate plane, find it by averaging the coordinates: the midpoint of (x1, y1) and (x2, y2) is (x1 + x22, y1 + y22).Geometry · Grade 8, Algebra 1, GeometryTriangleA triangle is a polygon with three sides and three angles. Its three corners are called vertices, and the angle measures in any triangle add to 180 degrees. Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse).Geometry · Grade 3, Grade 4, Grade 5MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Statistics · Grade 5, Grade 6, Grade 7SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3Isosceles TriangleAn isosceles triangle is a triangle with at least two sides of equal length. The equal sides are called legs, and the third side is the base. The two angles touching the base, the base angles, are always equal. If the angle between the legs is 40 degrees, each base angle is 70 degrees.Geometry · Grade 4, Grade 5, Grade 7AverageAn average is one number that stands for the typical size of the values in a data set. In everyday math, average means the mean: add all the values, then divide by how many values there are. In statistics, the median and the mode are also kinds of average.Statistics · Grade 5, Grade 6, Grade 7Right AngleA right angle is an angle that measures exactly 90 degrees, a quarter of a full turn. It looks like the corner of a square or a sheet of paper, and it is marked with a small square at the vertex. Two lines that meet at a right angle are perpendicular.Geometry · Grade 2, Grade 3, Grade 4RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6HeightHeight is how tall something is: the distance from its bottom to its top, measured straight up and down. In geometry, the height of a shape is the perpendicular distance from a base to the opposite vertex or side, so it always meets the base at a right angle. Area and volume formulas use it.Measurement · Grade 2, Grade 5, Grade 6Line SegmentA line segment is a straight part of a line with two endpoints. It starts at one point, stops at another, and includes every point between them. A segment with endpoints A and B is written AB. Unlike a line, which goes on forever, a segment has a definite length that you can measure.Geometry · Grade 4, Grade 5, Grade 6VertexA vertex is a corner point where two or more lines, rays, or sides meet. It is the point of an angle, a corner of a polygon such as a triangle, a corner of a solid, and the turning point of a parabola. The plural of vertex is vertices: a square has 4 vertices.Geometry · Grade 4, Grade 5, Grade 6