Explorations in Geometry

with the

Geometerís Sketchpad

Exploration 10

    1. Construct triangle ABC and find the geocenter where the medians intersect..
    2. Construct the perpendicular line segment to each of the sides, and label them x, y, and z; as above.
    3. Can you find a relationship between the lengths of segments x, y, and z and the triangle ABC. (hint, you need to take some more measurements )
    4. Find the area of Triangle ABG (G is the centroid) and compare to the area of ABC.
    5. Can you find other relationships between some of the triangle pieces that ABC has been cut into?
    6. What other geometric and/or algebraic relationships can you find in this figure?
    7. Write a brief paragraph explaining what you have found in this exploration. Remember to answer all the specific questions above.