GeoGebra Classroom

# GeoGebra Beginners

## GeoGebra Exercise (for beginners who think they know-it-all)

In this activity, you will create a segment and a line that passes through the midpoint of that segment that intersects that segment at right angles. We call this a perpendicular bisector. (Perpendicular - two lines intersect at right angles) (Bisector - "bi" means "two" and "sect" means "cut" so cut into two equal parts, or at the midpoint.) To begin, play around with the tools that are shown. Get familiar with them. When you think you are ready, go ahead and try to construct a perpendicular bisector of segment AB. Then answer the questions below. If you are stuck, there are more detailed instructions to follow. If you are still stuck, there is a video to help you through this. Good luck, and success!

## Working with GeoGebra - Practice for Beginners

What can you say about segments AB and AC? Explain your reasoning.

What can you say about segments BA and BC? Why? (Explain your reasoning)

What can you say about segments AC and BC? Why?

Depending upon how you labeled your points, you should have created triangle ABC. Based on the previous question, this triangle is equilateral. How would you classify quadrilateral ACBD? (Notice that the order of the letters is important. You can go clockwise or counterclockwise around the quadrilateral, but you may not zig-zag!)

Select all that apply
• A
• B
• C
• D
• E
• F

Construct line CD. Is segment CD the same length as two radii, AB? Explain your thinking.

What can you say about line CD in relation to segment AB?

## GeoGebra Exercise (with more detail for beginners who want or need help)

This applet shows only some of the many tools in GeoGebra. A video that follows these instructions is shown below. At any time, you can use the reverse arrow button in the top right corner to go back and redo. We start with two points, A and B. These are free points. You can move them anywhere with the move tool. They are blue. When doing constructions, all the tools are based on the compass and the straight edge. You could use the straight edge to draw a line segment from A to B. Do that with the segment tool. Make sure the segment starts and ends on the points A and B. The compass is used to make circles. Actually, it is how they anciently measured things anciently (using the radius of the circle). If you choose the compass tool (the one with the red circle) and click on it, it says "Select segment or two points for radius, then center point." Select that tool, then click on the segment AB itself, and move the circle around until you put its center at A. Note that a circle is the set of points (or "loci") that are equidistant (same distance, the radius) from a given point (the center). You should have two circles with centers at A and B, who both have a radius, AB. These two circles intersect twice. Use the intersection tool to make the intersection at the top point C, and at the bottom, point D. These two points are not blue. They are black. This is because they are dependent. They are linked to the intersection of the two circles. If you try to drag them... you can't. Try to drag A or B, and you can. Draw segments CA, CB, DA, DB, and CD. Then answer the questions.