## Pythagorean Theorem Proof 1

Move slider $\alpha$ to the extreme right.
1.) What do you observe? What is the area of the larger square (green and red regions)?

2.) Move slider p to the extreme right. What is the area of the figure formed in terms of a and b?

3.) What can you say about the area of the square in Question 1 and the area of the figure in Question 2?

4.) What equation can you form using the areas of these squares?

## 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.

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

## Deriving the Area of Parallelograms

Given below is a parallelogram with base b and height h. Move points A and B determine the shape and size of the parallelogram, and then move the red point to the extreme right and observe what happens.

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?

## Deriving the Area of Trapezoid

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

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 figure?
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?

## 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

## 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.

## 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.

## 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

## 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