Polygons with equal area

This applet is part of the lesson on Constructing Polygons with Equal Area posted in Mathematics for Teaching blog.


1. Drag point B. What do you notice about the area of the polygon?
2. Drag point A. What polygons are formed? What can be said about its area?
3. Drag points A and C to form a pentagon. 


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4. What must be true about C and D for the area of the pentagon to be equal to the area of the triangle.

Triangles and Quadrilaterals

Given
ABC is a triangle with base b and height h. Points D and E are midpoints of AB and BC, respectively.


Instructions
1. Move the slider h to determine the height of the triangle.
2. Move points A, B, and C to choose the shape of the triangle.
3. Move the circle in slider t to the extreme right transform the triangle into a quadrilateral.
4. Click check box to hide the triangle.

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Questions
1.) After moving slider t, what type of quadrilateral is formed?
1.) What is the relationship between the area of the triangle and the area of the quadrilateral?
2.) Find the area of the triangle in terms of b and h.
3.) Find the area of the quadrilateral in terms of b and h.

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Pythagorean theorem

Pythagorean Theorem: In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

view the GeoGebra applet in a new tab.




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Ferris Wheel

I am a little stressed out. I want to relax and ride on a GeoGebra Ferris Wheel.



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Click the Play button to turn the Ferris Wheel.

Sliders and Rhombuses

This construction demonstrates how a rhombus can be determined by a length and an angle given one point.


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Reduction and Enlargement

This applet shows the enlargement/reduction of a triangle with scale factor k and center O.




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Here are several of the activities that the teacher/student can do:

• The teacher may hide some elements in the objects (using the check box), and let the students predict the position of the missing objects.
• The students may use the distance, area and angle tools to investigate the relationship between the two triangles. 

Click here to download applet.

The Dancing Triangle

Move the vertices to determine the shape of your triangle and observe what happens.

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1. What do you observe when you move the three vertices?
2. Is there a relationship between the movement of the three vertices and the area of the triangle?
3. Move point R. What do you observe?
4. Explain why your observation in 3 is such. 

Download GGB file here.

Trigonometric Numbers

An applet that computes the trigonometric numbers of an angle.

View the applet in a new tab.
Download the applet.

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Approximating Pi

In the ancient times, there was no direct way to find the area of a circle. Mathematicians approximate it by using inscribed polygons.  Since it is possible to find the area of any polygon by dividing it into triangles, it is also possible to approximate the area of a circle by increasing the number of sides of the inscribed polygon.

To illustrate this concept, consider the circle with radius 1 as shown below.  To increase the number of sides of the inscribed polygon, move slider n to the right. What do you observe?

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As n increases, the area of the inscribed polygon approaches the area of the circle (Can you see why?). Intuitively, as we increase n, the better our approximation. As shown above, the area of the circle is approximately equal to 3.14....  This number is now known as the irrational number pi.

To download the applet, click here, and then click File>Save on your browser. 

Tracing the Derivative

Consider the function $f(x) = x^2 - 3x$. The number m is the slope of line a tangent to f at Point A. Point B is the ordered pair (n,m) where n is the x coordinate of A and m the slope of line a. Now drag point A along the graph. What do you observe? What can you say about the traces of point B?

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The graph of the traces of point B is the derivative function of f. Can you explain why?

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Technical Problems

For some reason, the GeoGebra applets have stopped displaying in my browser. I am not sure if it's the firewall of our university or a Google problem.  Please inform me if the applets do not also appear in your browsers.  

I'll post another applet as soon as the problem is fixed.

My apologies.