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    Geometric Mean

    Similar Right Triangles

    If you drop a perpendicular from the right angle of a right triangle to the opposite side, you will create three similar right triangles. This altitude is known as the geometric mean.

    Related: What are Similar Triangles | Theorems proving Similar Triangles| geometric mean | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity
      Geometric Mean example The geometric mean is any 'b' that can be expressed as
      in a proportion.

      To better understand how the altitude of a right triangle acts as a geometric mean in similar triangles, look at the triangle below with sides a, b and c and altitude H.
    Below is a picture of the many similar triangles created when you drop the altitude from a right angle of a right triangle.
    Diagram of Geomoetric mean
    Find the corresponding sides:
     Answer 

    AD &

    AD &
    Find the sides that correspond with AC
     Answer 

    AC &

    AC &
    Find the sides that correspond with BC
     Answer 

    BC &

    BC &


    Related: What are Similar Triangles | Theorems proving Similar Triangles| geometric mean | Side Splitter Theorem | Angle Bisector Theorem |Area & Similarity
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