Sunday, June 24, 2018

Task 2 - Drawing Similar Triangles (Part 2)

Task 2: Drawing Similar Triangles

In the applet below, A'B' = 2AB, A'C'= 2AC, and B'C'= 2BC. Use the Segment tool to draw ∆PQR such that PQ = 3AB, PR= 3AC, and QR = 3BC.



Questions

1.) How did you draw ∆PQR?

2.) What do you observe about the corresponding angles of the ∆ABC, ∆A'B'C' and ∆PQR?

3.) Based on Task 1 and Task 2, make a conjecture about your observations above.

Discussion

In Task 1 and Task 2, you have observed that it is easier to draw similar triangles if you make the corresponding sides of the triangles parallel. In addition, you have also observed that the corresponding angles of the triangles are congruent. For example,


and

.


In drawing the triangles, you made sure that the ratio of the lengths of corresponding sides is equal. In other words, you made the length of the corresponding sides proportional. For instance, the ratio of the lengths of the corresponding sides of to those of is 2. That is,


 


and 


Two triangles whose corresponding angles are congruent are called similar triangles. The lengths of the corresponding sides of similar triangles are proportional.


Task 1 - Drawing Similar Triangles (Part 1)

In the applet below, given ∆ABC, use the Segment tool to draw ∆A'B'C' such that A'B' = 2AB, A'C'= 2AC, and B'C'= 2BC.

Questions

1.) How did you draw ∆A'B'C'?

2.) What do you observe about the angles of the two triangles?

3.) Draw other triangles satisfying the same conditions and see if your observations hold.


Note 

In your lesson on Triangle Congruence, you have learned about corresponding angles and corresponding sides. In the two triangles above, the pairs of corresponding angles are A and A’, B and B’, and C and C’. The pairs of corresponding sides are AB and A’B’, BC and B’C’ and AC and A’C’.


Sunday, March 19, 2017

Visual Proof of Pythagorean Theorem

Shown below is a triangle whose sides form squares with sides a, b, and c.


1.) Move slider p to the extreme right.

What is the relationship among the squares when p was on the extreme left and the quadrilaterals when p was on the extreme right? 
2.) Move slider q to the extreme right. 

What is the relationship among the quadrilaterals when q was on the extreme left and when q was on the extreme right?   

3.) Move slider r to the extreme right.

What is the relationship among the quadrilaterals when r was on the extreme left and when r was on the extreme right?   

4.) Based on your exploration, what is the relationship among the areas of the squares with side lengths a, b, and c?

5.) Using the variables, a, b, and c write an equation about the relationship you found in 4.




Monday, July 11, 2016

Dice Rolling Simulation

Click the Roll Dice button and record the sum of the number of dots. Do this for 20 times and tally the result.

Questions

1.) What do you observe?
2.) Which sum occurs more often? less often?
3.) Do the simulation for 30 times, 40 times, 50 times, 100 times. Are your observations still the same?
4.) Explain why your observations are such.



Tuesday, July 22, 2014

The Infinite Chocolate Puzzle

View the video below and observe what happens. Can you tell where did the extra chocolate come from?


Now, explore the GeoGebra applet below by moving point A (up and down) and moving points B and C along the diagonal.

  1. What do you observe about the video and the applet?
  2. Are the video and applet similar? 
  3. Where did the extra chocolate come from? 
Thumbnail




 Created with GeoGebra by Guillermo Bautista

Tuesday, March 18, 2014

The Date Problem

You and a friend arrange to meet between 12:00 and 1:00 in the afternoon. After a week neither of you remembers the exact meeting time. As a result, it is possible for you arrive at random between 12:00 and 1:00 and waits exactly 15 minutes for your friend to arrive. After 15 minutes, each of you leaves if the other person has not arrived. What is the probability that the two of you will meet?

Click the Play button at the bottom left of the applet.


Explore!

1.) Click Pause and see the exact time the two friends arrive.
2.) Refresh the browser to delete the point traces.
3.) Click Pause and drag the sliders to customize the time arrival.

***

Problem by Erlina R. Ronda
Created with GeoGebra by Guillermo P. Bautista Jr

Thumbnail


Tuesday, June 18, 2013

GeoGebra Tutorial: Exporting GeoGebra Worksheet to HTML 5

GeoGebra worksheets cannot run on devices that do not support Java. Examples of such devices are Apple’s iPads. To address this limitation, GeoGebra has created an export feature to HTML5. In this tutorial, we learn how to export a GeoGebra worksheet to HTML5.

Steps in Exporting a GeoGebra Worsheet to HTML5

1. Open the GeoGebra worksheet that you want to export to HTML5.   

2. Click the File menu, select Export, and then select Dynamic Worksheet as Webpage (html).


2. In the Dynamic Worksheet dialog box, select Export as Webpage button.

3. Type the Title of the web page and the texts needed above and below the construction.

4. Select the Advanced tab and be sure to check the Export to HTML only and Remove Line Breaks check boxes



5. Select File: html in the File section

6. Click the Export button


The exported HTML file can be used as a web page or embedded to websites or blogs. The HTML5 page does not need Java in order to run.