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. 

The Parallel Postulate

In the figure below, AB and CD are parallel lines. EF is a transversal.

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

The parallel postulate states that given two parallel lines (on the same plane) and a transversal, their corresponding angles are congruent. Using this postulate as shown above, determine the measure of the other angles and record your observations. Make a conjecture about them.

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Polygons with equal area

This applet is part of the lesson on Constructing Polygons with Equal Area posted in Mathematics for Teaching blog.


1. Drag point B. What do you notice about the area of the polygon?
2. Drag point A. What polygons are formed? What can be said about its area?
3. Drag points A and C to form a pentagon. 


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4. What must be true about C and D for the area of the pentagon to be equal to the area of the triangle.