7.4 Midpoints and Medians in Triangles

Midpoints

 

A midpoint is the point in the middle of a line segment. To find it you find the length of the line and divide it by 2. When you join 2 midpoints in a triangle, which you will be doing lots of, the length of the 2 points will be half of the base of the triangle. For example in this diagram here the length of DE is half of the length of BC.

 

 

 

 

Medians

 

A Median is a line from the vertex of a triangle to the midpoint opposite to it. For example, the median here is the line from A to the midpoint of BC.

 

 

 

Key Terms

 

Centroid: The point where the medians of a triangle intersect.

 

Median: A line from the vertex of a triangle to the midpoint of the opposite line segment

 

Midpoint: The exact middle of a line segment.

 

Bisect: To divide into 2 equal parts. In the case of triangles, it is to divide a triangle into 2 equal triangles with the same area.

 

Right Bisector: A line that is perpendicular to a line segment and goes through it's midpoint.