A Geometric Construction

We'll construct a triangle and show that its three altitudes meet at a point (the orthocenter).
The completed GeoGebra file is here: Tutorial-1.ggb

Open a new, blank GeoGebra worksheet.

From the View menu, make sure Axes and Grid are unchecked and Algebra View is checked.

From the Options menu, select
Labeling > New Points Only.

Select the Line tool  and create the image shown to the right.
Hit the Esc key or select the Move tool .  See how you can move the points around.  The points are "free" but the lines are dependent.

Also, you can drag the labels around for better visibility.

See how your points and lines are represented in the Algebra View on the left.

Now we'll create the altitudes.  Select the Perpendicular Line tool ; see how instructions for using the tool are displayed on the tool bar.  Use this tool to make a picture like the one on the right.

If you need to delete an object you can select it then hit the Delete key.

To pan the worksheet, hold shift while dragging the mouse.  Alternatively, the Pan tool  is available.

To zoom in and out, use the mouse scroll wheel. Alternatively the zoom tools  are available.

Rename the altitudes as Alt1, Alt2, Alt3.  Just select the line (or click the object listed in the algebra view) then start typing.  Object names may not have spaces.

Now the labels Alt1, Alt2, Alt3 show up in the Graphics View.  Right-click them and uncheck "Show Label."

Select the Point tool and click the points where the triangle sides intersect with the altitudes.  Rename these points Foot1, Foot2, Foot3, and hide the labels.

It's a good habit to give your objects descriptive names.

Right-click any altitude again and select "Object Properties..."  The dialogue box to the right should appear. 

Ctrl-click Alt1, Alt2, Alt3 to select all three.  Click the Color tab and choose blue.  Click the Style tab and select a dashed line.  Close the Object Properties dialogue box.

Hide lines a, b, c by clicking the circles to the left of them in the Algebra View

Connect points A, B, C with segments, using the Segment tool

Using Object Properties, make these segments red and increase their line thickness.

As you move points A, B, C around, the feet of the altitudes can move off the triangle segments.  To obtain this effect we needed to define the triangle initial with lines instead of segments.

Lastly, let's emphasize that the feet meet the triangle sides with a right angle.

Select the Angle tool and put angle indicators at the feet.  Under Object Properties you'll want to modify these angles:
  • Hide the labels
  • Uncheck the "Allow Reflex Angle" option
  • Make smaller (make size = 20)
Again, as you move points A, B, C around, the feet may move off the triangle sides.  As a final touch, figure out how to indicate when a side has been "extended" to meet a foot, as shown in the picture to the right.

Some final thoughts...
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