Geometry
Chapter 5 Activity Lab
Spring 2009
Unit 5 Activity
Centroid of a triangle and quadrilateral. (to be used after section 5.3)
Goal: To find the centroid of a triangle and a quadrilateral using compass constructions .
Materials:
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2 pieces of cardboard (from drycleaners, works well)
Patty paper (tracing paper)
Compass, straightedge, colored pencils, markers.
SmartBoard questions
Motivation:
For an object to spin smoothly, its weight must be evenly distributed around is central axis (or rotation
axis) Balance on one foot. Lean forward. Why do you fall if you lean to far forward. Physically, there is
more mass forward that cannot be balanced. This can be modeled mathematically using centroids,
known as center of mass. A ratio between area of each side of the rotational axis and distance to
centroid must be balanced.
In Geometry, it is possible to construct the model for 2-D triangles and quadrilaterals by finding
centroids of triangles. (For any polygon, we can find centroids of triangles within the polygon, but it
becomes increasingly complex).
Activity 1: Triangle
1. Draw a scalene triangle
2. Find the midpoint of each side of the triangle.
a. Mark point only of each side
3. Draw the median (recall this is the line from a vertex to the midpoint of opposite side)
4. The centroid is the intersection. Mark this point.
5. Cut out the triangle. Balance it on the centroid.
6. Answer questions on SmartBoard on a sheet of paper to be turned in.
Activity 2: Quadrilateral
1. Draw a quadrilateral (approximately the size of patty paper)
2. Label ABCD on quadrilateral
3. Draw diagonal from A to C to make 2 triangles: ABC and CDA.
4. Mark midpoint of every side of the quadrilateral and the diagonal.
a. We now have midpoints of each triangle.
5. Locate the centroid of each triangle: Intersect the medians.
a. Using a marker, connect the 2 centroids.
6. Using patty paper , tape it to the cardboard (or alternative would be to erase all marks)
a. Trace the quadrilateral exactly.
Geometry
Chapter 5 Activity Lab
Spring 2009
b. Mark with pencil the midpoints on the sides of the quadrilateral.
c. Draw a new diagonal from B to D, making triangles: BCA and CDA
d. Reuse the midpoints from previous and find the altitudes of these 2 triangles (note that
our medians always intersect, so we coud just draw 2 lines, since 3rd median would
automatically intersect at the same point).
e. Mark the centroid of each triangle
i. Using a marker, connect the 2 new centroids.
7. Place patty paper on top of previous quadrilateral and look for intersection of the centroid line
here and the previous. Press with pen.