MEDIAN OF A TRIANGLE
Definition Of Median Of A Triangle
Median of a Triangle is a line segment joining a vertex of the triangle to the midpoint of the opposite side of the triangle.
More About Median of a Triangle
The three medians of a triangle are concurrent and the concurrent point is called the centroid of the triangle.
The centroid of a triangle divides the medians in the ratio 2:1, i.e. the length of the median from the vertex to the centroid is twice the length of the median from the centroid to the opposite side of the vertex.
Examples of Median of a Triangle
Video Examples: The Medians of a Triangle
Solved Example on Median of a Triangle
Ques: Identify the median of a triangle.
Choices:
A. 
B. 
C. 
D.
Correct Answer: A
Solution:
Step 1: Median of a triangle is a line segment from a vertex of the triangle to the midpoint of the opposite side of the triangle.
Step 2: is the only median drawn from the vertex A to the midpoint of the opposite side of
.
Step 3: So, is the median of a triangle.
Quick Summary
- A median connects a vertex to the midpoint of the opposite side.
- The three medians of a triangle are concurrent.
- The point of concurrency is called the centroid.
- The centroid divides each median in a 2:1 ratio.
🍎 Teacher Insights
Use physical models or dynamic geometry software to illustrate the properties of medians and the centroid. Emphasize the difference between medians, altitudes, and angle bisectors. Provide examples with coordinate geometry to find the midpoint and verify the 2:1 ratio.🎓 Prerequisites
- Basic Triangle Properties
- Midpoint of a Line Segment
- Line Segments
Check Your Knowledge
Q1: Which of the following is a median of triangle ABC?
Q2: The centroid of a triangle divides the median in what ratio?
Frequently Asked Questions
Q: What is the centroid of a triangle?
A: The centroid is the point where all three medians of a triangle intersect.
Q: What is the ratio in which the centroid divides the median?
A: The centroid divides the median in a 2:1 ratio, with the longer segment being from the vertex to the centroid.