Second Activity Using your triangle, construct the other two altitudes. What do you think will happen? Why? What do you observe for your own? How does it compare to the others? How does it compare to the conclusions angle bisectors and medians? Is there ever an instance when the orthocenter, the incenter and the centroid are the same point in the triangle? Explain. Performance Task: Triangular Inheritance A brother and a sister have inherited a large triangular plot of land. The will states that the property is to be divided along the altitude from the northern most point of the property. However, the property is covered with quicksand at the northern vertex. The will states that the heir who figures out how to draw the altitude without using the northern vertex, gets to choose his or her parcel first. How can the heirs construct the altitude? Is this a fair way to divide the land?
Second Activity Using your triangle, construct the other two altitudes. What do you think will happen? Why? What do you observe for your own? How does it compare to the others? How does it compare to the conclusions angle bisectors and medians? Is there ever an instance when the orthocenter, the incenter and the centroid are the same point in the triangle? Explain. Performance Task: Triangular Inheritance A brother and a sister have inherited a large triangular plot of land. The will states that the property is to be divided along the altitude from the northern most point of the property. However, the property is covered with quicksand at the northern vertex. The will states that the heir who figures out how to draw the altitude without using the northern vertex, gets to choose his or her parcel first. How can the heirs construct the altitude? Is this a fair way to divide the land?