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Geometry Problem 576: Unlocking the Power of Centroids: with a Focus on Quadrilaterals, Parallel Lines, and Proportions for High School and Math Education.

Given quadrilateral ABCD with centroids E and F of triangles ABC and BCD respectively, prove that (1) EF is parallel to AD, (2) the measure of EF is one-third of the measure of AD.

 

Centroid, Triangle, Quadrilateral

 

Problem 576

Centroids mark the point,
Parallel lines they anoint,
Proportions at each joint,
Geometry we'll never disappoint.

Points of interest we see,
EF and AD agree,
One-third is the key,
Mathematics is the degree.
 
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