Centroids Worksheet
Explore the concept of centroids in triangles, including medians and balancing points, with this Grade 6 math worksheet.
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Centroids in Triangles
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Read each question carefully and answer to the best of your ability. Show your work where necessary.
What is a Centroid?
The centroid of a triangle is the point where its three medians intersect. A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. The centroid is also the center of mass of the triangle, meaning if you were to cut out a triangle from a piece of cardboard, you could balance it perfectly on your finger at its centroid.
1. What is the centroid of a triangle?
The point where angle bisectors meet
The point where perpendicular bisectors meet
The point where medians intersect
The center of the inscribed circle
2. What is a median of a triangle?
A line segment from a vertex perpendicular to the opposite side
A line segment joining a vertex to the midpoint of the opposite side
A line segment that bisects an angle of the triangle
A line segment that connects two midpoints of the sides
3. The centroid is also known as the center of of the triangle.
4. Every triangle has exactly medians.
5. A median connects a vertex to the of the opposite side.
6. Explain why the centroid is sometimes called the 'balancing point' of a triangle.
7. Draw a triangle ABC. Then, draw all three medians and identify the centroid. Label the vertices A, B, C and the centroid G.
8. The centroid divides each median in a 1:2 ratio.
True
False
9. All three medians of a triangle intersect at a single point.
True
False
Refer to the image below for the next question:
10. If this triangle instrument were made of a uniform material, where would you expect its balancing point to be?