Constructing the Medians and Altitudes of Triangles

Author:: Harrison Bosher, Amy Springstead, Terry Lee Lindenmuth, Tim Brzezinski

Which previously learned construction does the applet above showcase?

Select all that apply

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.

Median

What is a median of a triangle?

Select all that apply

a line segment drawn from a vertex to the midpoint of the opposite side

a line segment or ray drawn from a vertex that cuts the angle in half

a line drawn perpendicular to a side of the triangle through its midpoint

What is an altitude of a triangle?

Select all that apply

A
a line segment drawn from a vertex perpendicular to the opposite side (or the line containing that side)
B
a line segment drawn from a vertex to the midpoint of the opposite side
C
a line segment or ray drawn from a vertex that cuts the angle in half
D
a line drawn perpendicular to a side of the triangle through its midpoint

Let's construct the altitude that intersects the vertex B. What is the name of the side (or line) that the altitude will intersect?

Select all that apply

Using the ideas we have discussed in the previous questions, try to construct a median of triangle ABC using vertex A.