Centroids Exploration Worksheet
Explore the concept of centroids in triangles, including finding medians and the point of concurrency.
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Centroids Exploration Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
A centroid is the geometric center of a plane figure. For a triangle, it's the point where the three medians intersect. A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.
The image illustrates a triangle with its medians drawn, intersecting at the centroid. The centroid divides each median into two segments with a 2:1 ratio.
1. What is the definition of a median in a triangle?
A line segment connecting two vertices.
A line segment from a vertex to the midpoint of the opposite side.
A line that bisects an angle.
A line perpendicular to a side.
2. What is the special point where all three medians of a triangle intersect?
Incenter
Circumcenter
Centroid
Orthocenter
3. The centroid divides each median into two segments with a ratio.
4. To find the midpoint of a side, you can use the midpoint formula: .
5. Consider a triangle with vertices A(1, 4), B(5, 2), and C(3, 6). Find the midpoint of side AB.
6. The centroid is always located inside the triangle.
True
False
7. Explain why the centroid is sometimes referred to as the 'center of mass' of a triangle.