In this lesson, you will use GeoGebra (file below) to construct an altitude and a perpendicular bisector of a triangle. Directions: Step 1 Select the line segment icon. Using the line segment tool, create ABC .
** The first construction will be of an altitude (base = BC). (All triangles have 3 altitudes).
Step 2
Select the perpendicular line icon. Note: An altitude is a line that is perpendicular to a/the base and passes through the highest point (opposite vertex) . With the perpendicular line icon selected, click on point A, then move the cursor over side BC until it is highlighted (darkens), then click on side BC. (If the triangle is an acute triangle, the altitude will be inside the triangle.)
** The next construction, you will be of a perpendicular bisector (base = BC). (All triangles have 3 perpendicular bisectors).
Step 3
Select the midpoint (center) icon. Place the cursor over side BC until it is highlighted (turns dark), then left-click on it. This should create point D, the midpoint of side BC.
Step 4
Select the perpendicular line icon. Note: A perpendicular bisector is a line, (ray or segment), that bisects the base and is perpendicular to the base. Left-click on point D then place the cursor over side BC until it is highlighted (turns dark), then click on side BC.
Step 5
INVESTIGATE Move vertices (points) A, B, and C, around in the drawing area. Question 1: Are the altitude and the perpendicular bisector the same line? Question 2: Can they ever be? If so, under what circumstances?
Step 6
INVESTIGATION (CONT) Right-click on any object and bring up the “properties” dialogue box. Click on segment c (side CA) to select it. Then place a check in the “show label” box. From the drop-down menu, select “Value”. This will display the measure of side CA. Repeat this for side BA. Then, close the properties box. Repeat the earlier investigation and answer the question: Move vertices (points) A, B, and C, around in the drawing area. Question 1: Are the altitude and the perpendicular bisector the same line? Question 2: Can they ever be? What type of triangle?