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Center of Mass. (a) Prove that each median of a triangle divides the triangle into two subtriangles of equal area. (b) Use the result from (a) to explain why the centroid is the center of mass of the triangle. In other words, explain why a triangle made of a rigid, uniformly dense material would balance at the centroid.

Center of Mass. (a) Prove that each median of a triangle divides the triangle into two subtriangles of equal area. (b) Use the result from (a) to explain why the centroid is the center of mass of the triangle. In other words, explain why a triangle made of a rigid, uniformly dense material would balance at the centroid.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Solve using euclid geometry. Include helpful diagrams. 

**Center of Mass.** (a) Prove that each median of a triangle divides the triangle into two subtriangles of equal area. (b) Use the result from (a) to explain why the centroid is the center of mass of the triangle. In other words, explain why a triangle made of a rigid, uniformly dense material would balance at the centroid.
Transcribed Image Text:**Center of Mass.** (a) Prove that each median of a triangle divides the triangle into two subtriangles of equal area. (b) Use the result from (a) to explain why the centroid is the center of mass of the triangle. In other words, explain why a triangle made of a rigid, uniformly dense material would balance at the centroid.
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