Constructing the Medians and Altitudes of Triangles
Which previously learned construction does the applet above showcase?
What is significant about the two circles drawn in the construction? What do you notice about each circles radius? How about their centers?
In your own words, write the steps for constructing the perpendicular bisector of the segment AB.
What is a median of a triangle?
Let's construct the median from vertex A. What is the name of the opposite side that the median will intersect?
Which previously learned construction can we apply in order to find the midpoint of the opposite side?
Using the ideas we have discussed in the previous questions, try to construct a median of triangle ABC using vertex A.
Describe the steps you took in order to construct the median. Be as specific as possible.
What is an altitude of a triangle?
Let's construct the altitude that intersects the vertex B. What is the name of the side (or line) that the altitude will intersect?
What previously learned construction can we apply to intersect the opposite side perpendicularly?
Using the ideas we have discussed in the previous questions, try to construct an altitude of triangle ABC using the vertex B.
Describe the steps you took in order to construct the altitude. Be as specific as possible.