## Wednesday, March 28, 2012

### 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.

***

## Saturday, March 24, 2012

### 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.

## Wednesday, March 21, 2012

### 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

## Friday, March 16, 2012

### 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.

## Tuesday, March 13, 2012

### Fibonacci Numbers and the Fibonacci Spiral

Fibonacci Numbers and the Fibonacci Spiral - GeoGebra Dynamic Worksheet
 This is one applet for constructing Fibonacci Squares and the Fibonacci spiral. The Fibonacci spiral is made up of quarter-circular arcs whose radii are consecutive Fibonacci numbers. You can read detailed instructions under the applet, short instructions at the left side of the applet, or see video instructions by following the link below. The order of steps is important. Video Instructions Click on the Quarter Circle button. Click on the green square to create a square under it (the color will change). Drag the green square to align the blue point with the free end of the quarter circle. Rotate the green square by dragging the red point. We want to align the red side of the green square with the radius of the quarter circle. Click the Increase button until the side of the square equals the sum of the sides of the previous two squares. Repeat the procedure from step 1.

## Saturday, March 10, 2012

### Line through Two Points

Move sliders m and b to approximate the line that passes through the two points.
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 applet above shows that given two points, a line maybe drawn through them which is the first postulate of Euclid.

## Sunday, March 4, 2012

### Odd Number Theorem

Move the slider and observe what happens.

1. How many 1 by 1 squares are added each time the slider increases by 1?
2. What is the total number of colored squares 1 by 1 if n = 3, 4, 5?
3. What can you generalize from your observations in 1 and 2?

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 applet above shows the sum of the first n odd integers is n2.