Explorations in Geometry

with the

Geometer’s Sketchpad

Exploration 10

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