## 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?