Wednesday, October 17, 2012

Guess the Equation of the Line

Consider the graph of a linear function in the applet below. 
  1. Move sliders a and b to guess the equation of the graph. 
  2. Click the check box to check your answer. 
  3. Click the New Line button to generate a new line.

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
Guillermo Bautista, Created with GeoGebra


Sunday, October 14, 2012

Quadrilateral Angle Sum

Move points A, B, C or D to create the desired quadrilateral. Move the slider to the extreme right.  As each slider appears, rotate the quadrilateral by moving it to the extreme right. 
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
Guillermo Bautista, Created with GeoGebra

The applet above demonstrates that the angle sum of a quadrilateral is 360 degrees. 

Snapshot


Wednesday, October 10, 2012

Multiplication of Fractions

The applet below illustrates the visual representation of multiplication of fractions. Move the sliders to explore 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

Guillermo Bautista, Created with GeoGebra


Snapshot

Wednesday, October 3, 2012

Pythagorean Theorem Proof 2

Given: Triangle with sides a and b and hypotenuse c and three squares containing a, b and c. 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
Guillermo Bautista, Created with GeoGebra

Questions 

  1. What are the areas of the green square and the red square? 
  2. Move slider p to the extreme right. What types of quadrilaterals were formed from the two squares? 
  3. What can you say about the areas of squares in Question 1 and the areas  of quadrilaterals in Question 2?
  4. Move slider q to the extreme right. What type of quadrilaterals were formed? 
  5. What can you say about the quadrilaterals formed in Question 1 and the quadrilaterals in Question 4?
  6. Move slider r to the right. What do you observe?
  7. What can you say about the areas of the red square,  green square, and the area of square containing c?
  8. In terms of a, b, and c, what equation can be formed relating the areas of the three squares?
Snapshot