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GeoGebraClasse GeoGebra

Properties of the median

  • Median: In a triangle ABC, the median from A to BC (where M is the midpoint of BC) divides the triangle into two equal-area triangles:
  • Centroid (G): The intersection of the three medians is called the centroid or center of gravity. Key properties:
    • The centroid divides each median in the ratio AG:GM=2 (from vertex to base).
    • The three larger triangles with vertex at G and sides along the vertices of the original triangle have equal areas:
  • 1.

    In triangle ABC, M is the midpoint of BC. Prove that .

    2.

    In triangle ABC, M is the midpoint of BC. If =24, find

    3.

    In triangle ABC, let G be the centroid. If  , ..................

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    4.

    In triangle ABC, let G be the centroid. If , the area of the triangle BCG is: .........

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    5.

    Construct the medians BN and CP. Find the ratio of the areas of triangles GNC and GAP.

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