## Thursday, December 6, 2012

## Sunday, December 2, 2012

### The Inscribed Angle Theorem

In the figure below, angle

Check the

Snapshot

*BAC*is an inscirbed angle and angle*BOC*is the central angle of circle*O*. Both angles are subtended by the same arc. Make a conjecture about these two angles.Check the

*Show/Hide Angle Measures*check box and move any of the points. Is your conjecture always correct? Prove your conjecture.Snapshot

## Wednesday, November 21, 2012

### GeoGebra Tutorial: Using the Perpendicular Line and the Point on Object Tools

In this tutorial, we use GeoGebra
to explore the minimum sum of the distances of a point on the interior of a
triangle to its sides. We learn how to use the

Steps in Creating the Applet

*Point on Object*tool and the*Perpendicular Line*tool. We also learn how to compute using the Input bar. The final output of this tutorial is shown in the following applet.Steps in Creating the Applet

## Thursday, November 15, 2012

### Circumcircle and Circumcenter

Click the check boxes and move the vertices of the triangle to explore. What do you observe?

In any triangle, a circle called

In any triangle, a circle called

*circumcircle*maybe drawn that passes through its vertices. The center of the circumcircle is called the*circumcenter*. The perpendicular bisector of the three sides of any triangle passes through its circumcenter.## Wednesday, November 7, 2012

### Napoleon's Theorem

In the applet below,

1) What do you observe about the figure?

2) Move points

The Napoleon theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those triangles themselves form an equilateral triangle.

*ABC*is a triangle whose sides are also sides of equilateral triangles that contain the green line segments. Points*P*,*Q*, and*R*are centroids of the equilateral triangles.1) What do you observe about the figure?

2) Move points

*A*,*B*, and*C*. Are your observations still the same?The Napoleon theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those triangles themselves form an equilateral triangle.

## Wednesday, October 17, 2012

### Guess the Equation of the Line

Consider the graph of a linear function in the applet below.

Guillermo Bautista, Created with GeoGebra

- Move sliders
*a*and*b*to guess the equation of the graph. - Click the check box to check your answer.
- Click the
*New Line*button to generate a new line.

Guillermo Bautista, Created with GeoGebra

## Sunday, October 14, 2012

### Quadrilateral Angle Sum

Move points

Guillermo Bautista, Created with GeoGebra

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

Snapshot

*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.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.

Snapshot

Guillermo Bautista, Created with GeoGebra

Snapshot

## Wednesday, October 3, 2012

### Pythagorean Theorem Proof 2

Given: Triangle with sides

Guillermo Bautista, Created with GeoGebra

*and***a***and hypotenuse***b****and three squares containing***c***,***a***and***b***.***c*Guillermo Bautista, Created with GeoGebra

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

Snapshot

## Friday, September 28, 2012

### Pythagorean Theorem Proof 1

Instructions/Questions

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

Guillermo Bautista, Created with GeoGebra

Snapshot

## Thursday, September 27, 2012

### The SSS Triangle Congruence

To construct a triangle congruent to triangle

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.

*ABC*, move the slider to the right. To see the construction steps, move the slider slowly to the extreme right.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

Guillermo Bautista, Created with GeoGebra

Questions

*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.Guillermo Bautista, Created with GeoGebra

Questions

- If the red point is on the extreme right of the segment, what shape is formed? Justify your answer.
- What is the area of the shape in Question 1?
- How is the area of the shape in Question 1 related to the area of the original figure?
- What is the area of the parallelogram in terms of
*b*and*h*? - 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

Guillermo Bautista, Created with GeoGebra

Questions

*b*_{1}and*b*_{2}and height*h*. Move the slider to the extreme right and observe what happens.Guillermo Bautista, Created with GeoGebra

Questions

- When alpha is 180 degrees, what shape is formed? Justify your answer.
- How is the area of the shape in 1 computed based on the given?
- What is the relationship between the area of the shape in 1 and the area of the trapezoid?
- 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

3.) In the

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.

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