Constructing the Medians and Altitudes of Triangles

Which previously learned construction does the applet above showcase?

Perpendicular lines Perpendicular Bisector Copy of angle Angle Bisector

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.

[color=#0000ff][b][u][size=150][size=200]Median[/size][/size][/u][/b][/color]

What is a median of a triangle?

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 [*]a line segment drawn from a vertex perpendicular to the opposite side[/*][*][/*]

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.

[size=200][color=#0000ff][u][b]Altitude[/b][/u][/color][/size]

What is an altitude of a triangle?

a line segment or ray drawn from a vertex that cuts the angle in half a line segment drawn from a vertex perpendicular to the opposite side (or the line containing that side) a line segment drawn from a vertex to the midpoint of the opposite side 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?

AB AC BC

What previously learned construction can we apply to intersect the opposite side perpendicularly?

Discussion Time!

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.

Constructing the Medians and Altitudes of Triangles

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

Using the ideas we have discussed in the previous questions, try to construct an altitude of triangle ABC using the vertex B.

Information: Constructing the Medians and Altitudes of Triangles