Unit 2, Lesson 13
Weighted Averages in a Triangle
Integrated Math 2
13.1
Warm-up
Triangle is graphed.
Find the midpoint of each side of this triangle.
Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Triangle is graphed.
Find the midpoint of each side of this triangle.
Your teacher will tell you how to draw and label the medians of this triangle.
Here is a triangle with its medians drawn in. A median is a line segment drawn from a vertex of a triangle to the midpoint of the opposite side. Triangles have 3 medians, with 1 for each vertex.
Notice that the medians intersect at 1 point. This point is always of the distance from a vertex to the opposite midpoint. Another way to say this is that the point of intersection, , partitions segments and so that the ratios and are all .
We can prove this by working with a general triangle that can represent any triangle. Since any triangle can be transformed so that 1 vertex is on the origin and 1 side lies on the -axis, we can say that our general triangle has vertices , and . Through careful calculation, we can show that all 3 medians go through the point . Therefore, the medians intersect at this point, which partitions each median in a ratio from the vertex to the opposite side’s midpoint.
A median is a line drawn from a vertex of a triangle to the midpoint of the opposite side.
Each dashed line segment in this image is a median.