Triangle Angle Sum Proof 2

1.) Move the vertices of the triangle to determine the shape and size of the triangle you want.
2.) Move the slider to the extreme right. What do you observe?
3.) What is the relationship between the three angles which meet at a point, and the three interior angles of a triangle?
4.) What can you say about the angle sum of the parallelograms/trapezium formed?
5.) Make a conjecture about your observation.

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Another demonstration that shows that the sum of the interior angle of a triangle is 180°.

Blogineering: Our new blogging tutorial site

Blogineering is a new blog that Riley Ayes and I created for helping new bloggers start and grow a blog. Riley (my best friend in High School) is a civil engineer, so it is pretty obvious who thought of the name.

If you search the word ‘blogineering’ on the net (we actually never knew that such word exists before we thought of the name), you’ll find that it refers to blogs about science, engineering, and technology. However, we are giving it a new meaning. We combined the words blog and engineering to refer to ‘creating and growing a blog systematically — that is engineering blogs.’

The ASA Triangle Congruence

In the figure below, the angles of triangles 1 and 2 which have the same color are congruent.  The side between the two angles of the two triangles are also congruent.

1. Move the vertices of triangle ABC. What do you observe?
2. Use the tools provided to investigate the triangle. List your observations. 
3. Make a conjecture of what you have observed. 

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The ASA triangle congruence postulate (actually, it's a theorem), states that if the two corresponding angles of two triangles are congruent, and the corresponding included sides are congruent, then the two triangles are congruent.

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This article is sponsored by Euroffice for office whiteboards.

Parabola by Definition

Drag point C along the line. What do you observe? What shape is formed by the traces of the the point.


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A parabola is a locus of points that are equidistant to a given point (focus) and a given line (directrix).

Origami: Getting the Square Root of a Number

A rectangular piece of paper is folded in the middle, horizontally and vertically, to denote the rectangular coordinate axes. Another fold is made to denote y = - 1. Two points are constructed -- Point M on (0,1) and point P on (0,-n).

Fold the paper through P (by moving point P in the applet) such that point M is on y = -1 (by moving point Q in the applet).


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Problem: Prove that if point P is at (0,-n), then the intersection of the fold and the x-axis is at .

The discussion of the mathematics behind this applet and the ggb file will be available for download this week at Mathematics and Multimedia.

Relflecting the Exponential Function

The green curve is the graph of the function f(x) = e^x. The blue line is the graph of the function g(x) = x.  Point A is on f, and A' is the reflection of A along the graph of g(x). 

1.) Drag point A along f and observe the red trace.
2.) What are the coordinates of the reflection of point A coordinates (a,b)?

3.) What do you think is the equation of the graph traced by A'?

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Multiplication in Parabola

Move the points of on the parabola and observe the coordinates of the points on the axes.
What conjecture can you make from your observation?


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


Exercise: Prove your conjecture above.

The Wittgenstein Rod

Instructions:

1.) Move the red point to determine the fixed pivot point.
2.) If we move the point on the circle, what shape will be formed?
3.) Try moving the point. What shape was formed?
3.) Repeat 1-3 several times for different positions of the fixed point.




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The Wittgenstein rod is a thought experiment proposed by Ludwig Wittgenstein. The problem is as follows: One end of a rod is attached to a circular track.  The rod passes through a fixed pivot point (the red point).  As one end of the rod traces the circle, what is the shape traced by the other end (the green point)?

Largest Equilateral Triangle

What is the largest equilateral triangle that can be cut from a square with side length 1 unit. Drag points P and Q to find out.




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You may want to see more than 50 step-by-step GeoGebra tutorials at Mathematics and Multimedia.

July 2011 Top Posts

Here are the most popular posts for July 2011. Enjoy exploring. 

1. The Pantograph
2. Circle Approximation Graph
3. Viviani's Theorem created with GeoGebra 4.0 beta
4. Circles and Arbelos
5. Triangles and Quadrilaterals
6. Visualizing Multiplication of Fractions
7. The GeoGebra 4.0 Sneak Peek Series
8. Approximating the area of a circle
9. The Eutrigon Theorem
10. Circumcenter of a Triangle

Linear Approximation of a Function

In the textfield you can input the function you want.

Double click the applet to open it in a new window.

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


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