Friday, September 28, 2012

Pythagorean Theorem Proof 1

Instructions/Questions
  1. Move slider alpha to the extreme right. What do you observe? What is the area of the larger square?
  2. Move slider p to the extreme right. What is the area of the figure formed? 
  3. Move slider q to the right to verify your answer in Question 2. 

  4. 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


  • What can you say about the area of the square in Question 1 and the areas of the two squares in Question 2? What equation can you form using the areas of these squares?  


  • Snapshot

    Thursday, September 27, 2012

    The SSS Triangle Congruence

    To construct a triangle congruent to triangle ABC, move the slider to the right. To see the construction steps, move the slider slowly 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

    When n = 16, move the vertices of triangle ABC. What do you observe? 

    The applet above shows that if the three corresponding sides of two triangles are congruent, then the two triangles are congruent. 

    Snapshot

    Tuesday, September 25, 2012

    Deriving the Area of Parallelograms

    Given below is a parallelogram with base b and height h. Move the two blue points to determine the shape and size of the parallelogram, and then move the red point to the extreme right 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
    Guillermo Bautista, Created with GeoGebra

    Questions

    1. If the red point is on the extreme right of the segment, what shape is formed? Justify your answer. 
    2. What is the area of the shape in Question 1? 
    3. How is the area of the shape in Question 1 related to the area of the original figure?
    4. What is the area of the parallelogram in terms of b and h
    5. What can you conclude about the area of the parallelogram in the original figure and the area of the shape in Question1? 

    Snapshot


    Monday, September 24, 2012

    Deriving the Area of Trapezoids

    Given below is a trapezoid with bases b1 and b2 and height h. Move the slider to the extreme right 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

    Guillermo Bautista, Created with GeoGebra

    Questions

    1. When alpha is 180 degrees, what shape is formed? Justify your answer. 
    2. How is the area of the shape in 1 computed based on the given? 
    3. What is the relationship between the area of the shape in 1 and the area of the trapezoid?
    4. What formula will describe the area of the trapezoid based on the given above? 
    Snapshot


    Friday, September 21, 2012

    Events

    UPCOMING EVENTS


    Title: Using GeoGebra in Teaching Mathematics (Batch 2)
    Date: 15-17 July, 2016
    Venue: University of the Philippines (Baguio)
    Title: Using GeoGebra in Teaching Mathematics (Batch 1)
    Date: 8-10 July, 2016
    Venue: University of the Philippines (Baguio)
    PAST EVENTS
    Title: GeoGebra for Better Teaching and Learning
    Date: October 6, 2012
    Venue: St. Therese College, Pasay City
    No. of Participants: 31
    Title: Training-Seminar on Teaching with GeoGebra for Marinduque State College Students
    Date: February 14-15,2012
    Venue: STTC Building, UP NISMED, University of the Philippines, Diliman
    No. of Participants: 25
    Title: Introductory Course on the Use of GeoGebra in Teaching and Learning Mathematics
    Date: May 5-6, 2011
    Venue: Vidal Tan Hall, UP NISMED, University of the Philippines, Diliman
    No. of Participants: 21
    Title: Lesson Study for Teaching through Problem Solving with GeoGebra
    Date: May 9-13,2011
    Venue: STTC Building, UP NISMED, University of the Philippines, Diliman
    No. of Participants: 20
    Title: Using GeoGebra in Teaching and Learning Mathematics
    Date: August 6, 13, 20,2011
    Venue: Vidal Tan Hall, UP NISMED, University of the Philippines, Diliman
    Number of Participants: 25

    Thursday, September 20, 2012

    How to Embed An Applet in a Blogspot Post

    Starting October 2012, the GeoGebra Institute of Metro Manila (GIMM) will be accepting post contributions from GeoGebra users in the Philippines. To those who are interested to share their applets, the tutorial below provides step by step instructions on how to upload applets in Blogspot, the platform used by GIMM. If you are interested to join, please email upnismedmultimedia@gmail.com 

    Embedding an Applet in a Blogspot Post

    1.) Open the GeoGebra worksheet that you want to embed in a Blogspot post. 

    2.) Export the GeoGebra worksheet as HTML. This will display the exported worksheet as an applet in a web browser.


    3.) In the web browser where the GeoGebra applet is displayed, right click a blank space outside the applet and the select View Source or View Page Source. This will display the HTML source code of the applet in another window or tab.

    4.) In the source code window, copy the applet code; that is, copy the text from <applet> to </applet>


    5.) Open the Blogspot post where the applet is to be inserted, and then select the HTML button to display its HTML view.

    6.)  Paste the applet code on a location that you want it to appear 

    7.) Select the Compose button to go back to the text view or click the Preview button to view how the applet will look like.

    8.) Click the Save button.  

    Monday, September 17, 2012

    Tutorial 6 - Exporting Worksheet as HTML

    It is possible to export a GeoGebra worksheet as an HTML web page. HTML webpages can be uploaded in websites as a stand alone page. 

    To explort w Worksheet as a Dynamic HTML, do the following:

    1.) Open the GeoGebra file that you want to export as HTML.
    2.) Select the File menu, click Export, and then click Dynamic Worksheet as Web Page(html).  




    3.) In the Dynamic Worksheet Export dialog box, select Export as Webpage tab. 



    4.) In the Export as Webpage tab, type the title of your worksheet in the Title text box, and then click Export when done.  This will open the Save dialog box.

    5.) In the Save dialog box, type the name of your file and then click the Save button.

    Saving the file will automatically open the HTML on your browser. 


    Tuesday, September 11, 2012

    A Visual Proof of the Pythagorean Theorem

    Move point E to determine the shape of the triangles, and then move slider α 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 , September 11, 2012, Created with GeoGebra

    Questions:

    1. What is the relationship among the areas of squares with side lengths a, b, and c
    2. What equation describes the relationship among the areas of the three squares? 
    3. Prove that the green quadrilateral inside the large when  α is  90° is a square
    Snapshot


    Thursday, September 6, 2012

    The Missing Square

    Move the slider to the extreme right 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
    Guillermo Bautista, Created with GeoGebra

    Where is the missing square?

    Snapshot



    Archive

    Monday, September 3, 2012

    Free, Semi-free, and Dependent Objects

    In GeoGebra, an object may be free, semi-free, or dependent. It is important to understand the differences among the three to perform effective geometric constructions.

    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


    A free object does not depend on any object. You can move a free object anywhere on the Graphics view. In the figure above, points O and C are free objects. Point O determines the center of the circle which can be placed anywhere, and point C determines its radius.

    A semi-free object, on the other hand, depends on one object. Semi-free objects can be moved but with restrictions. In the applet above, point A is a semi-free object. It can move, but only along the circumference of the circle.

    Lastly, a dependent object depends on two or more objects. Unlike the other types of objects mentioned above, it cannot be moved by the mouse. For instance, point B above depends on point A and point C. Since it is the midpoint of points A and C, it will only move if point A or point C are moved. 

    Exercise: In the applet Exploring Triangles, identify the free, semi-free, and dependent objects.

    Snapshot