Day 3 Altitudes and Perpendicular Bisectors
Objectives:
1) Definition of altitude and Definition of perpendicular bisector
2) Proper Construction of altitude and Proper Construction of
perpendicular bisector
1) Definition of altitude
A perpendicular segment in which one endpoint
is at a vertex and the other endpoint is on the side opposite
that vertex
(Remind the students that perpendicular mean forming right
angles)
Definition of perpendicular bisector
A segment or line that contains the
midpoint of a side of the triangle and is perpendicular to that
side
2) Construct the altitude and perpendicular bisectors
First show how to construct with compass and straightedge
Then show how to use GSP to construct the altitude and the
perpendicular bisector. Click here for a step by step example
of each.
Construct the a median together with the students, then have
the students construct the remaining medianshave them figure out
what determines the number of altitudes and perpendicular bisectors
a triangle has.
Have the students explore the altitudes...do they always fall
in the interior of the triangle
3) Have the students discuss the difference between medians,
altitudes and perpendicular bisector
Is there a time when the a median and an altitude of a triangle
can be the same segment?