Midsegmens and Congruent Triangles

A midsegment of a triangle is a segment that connects the midpoints of any two sides of the triangle. This applet demonstrates that the three midsegments of any triangle divide the original triangle in four congruent triangles. The demonstration is based on the following properties:

1. The midsegment is parallel to the third side of the triangle. 
2. Any parallelogram has a rotational symmetry with center the intersection point of the diagonals and angle of rotation 180∘

Irina Boyadzhiev, 9 February 2014, Created with GeoGebra

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The Area of the Median Triangle - Dynamic Proof

Let ABC be a given triangle. The triangle with sides equal to the medians of ABC is called the Median Triangle.
We will show that the area of the median triangle is 3/4 of the area of the original triangle ABC.

•  Drag the two sliders to the end to construct the median triangle by translating the medians.

To rearrange the area of the median triangle:

• Click the Rearrange checkbox. This will show a green point at the vertex of the median triangle. 
•  Drag the green point to C.
•  Drag the green point at B to M_c. 
• Drag the green point at M_a to M_c. 

Irina Boyadzhiev, 29 January 2014, Created with GeoGebra

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Pythagorean Theorem

Irina Boyadzhiev, 13 December 2013, Created with GeoGebra

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Vertical Line Test

This applet can be used to determine whether one relation is a function or not by using the Vertical Line Test. The Vertical Line Test says that if some vertilcal line meets the graph in more than one point then the relation is not a function.

•  In the input box enter a polynomial equation of x and y in the form "polynomial = number".
  For example, to graph y = x², enter y - x² = 0 
• Drag the slider to use the vertical line test.

Irina Boyadzhiev, 25 September 2013, Created with GeoGebra

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