Day 3 ­ Altitudes and Perpendicular Bisectors

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 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?

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