Overlapping Squares II

1.) Move the red point. What do you observe?
2.) What can you say about the green and the blue triangles?
3.) Make a conjecture about the triangles.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

4.) Click the Show Blue Point  check box to show the blue point at the upper right vertex of the bigger square.
5.) Move the point to rotate the triangle.Did your conjecture hold?

6.) Challenge: Prove your conjecture.

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Overlapping Squares

Move the blue point and observe what happens.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1. Make a conjecture about the area of the overlapping regions.
2. Prove  your conjecture.

The Angle Trisector

In the figure below, |AB| = |BD| = |CD|. Move point P and observe the figure.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1. What kind of triangle is triangle BDC?
2. Make a conjecture about the relationship between angle PDC and angle PAB. 
3. Verify your conjecture by clicking the Show Angles Measures check box.
4. Challenge: Prove your conjecture

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Systems of Linear Equations

Move the sliders a, b, c and d to explore the graphs of the linear functions y = ax + b and y = cx + d.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1. When are the graphs coinciding? intersecting? parallel?
2. Describe the relationship between the appearance of the graphs and the parameters a, b, c, and d.
3. Is it possible to adjust the sliders such that the two lines are perpendicular? Justify your answer.