median of a triangle Chapter 6 (p. 310)
A segment from a vertex of a triangle to the midpoint of the opposite side
To find the median of a triangle, follow these steps:
1. Draw the triangle: Start by drawing the triangle on a piece of paper or using a geometry software.
2. Identify the vertices: Label the vertices of the triangle as A, B, and C.
3. Find the midpoint of one side: Choose one side of the triangle and find its midpoint. To do this, you can draw a line segment from one endpoint of the side to the midpoint of that side. This line segment is called the median of the side.
4. Repeat for the other sides: Find the midpoints of the other two sides using the same method.
5. Draw the medians: Draw each median from its respective vertex to the midpoint of the opposite side.
6. Find the point of intersection: The point where all three medians intersect is called the centroid of the triangle.
7. Measure the length of the median: Measure the length of each median from the vertex to the midpoint of the opposite side.
The length of the median is the distance between the vertex and the midpoint of the opposite side. The median of a triangle divides the triangle into two equal areas, and the centroid is the center of gravity of the triangle.
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