Constructing congruent triangles

Move the slider to the right one step at a time and observe what happens.

1.) After the construction, move any of the vertices of triangle ABC. What do you observe?
2.) How is the construction similar to the manual compass and straightedge construction?
3.) Which of the congruence postulates of triangles does the construction show?

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

The construction above is a simulation of constructing a triangle congruent to a given triangle using compass and straightedge.

Download GGB file at GeoGebraTube.

Constructing Similar Triangles

1.) Move the slider to the right to construct a triangle similar to triangle ABC.
2.) Using the tools on the toolbar to compare the measure of the interior angles, side lengths, and areas of the two triangles. What do you observe?

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3.) Move the vertices of triangle ABC. Do your observations still hold?
4.) Make conjectures based on your observations and prove your conjectures.

Download GGB file 

Parallelogram Area Proof

1. Move H to the rightmost part of the segment.
2. What is the relationship between the area of the parallelogram to the area of the rectangle? Why?

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This applet illustrates that the area of a parallelogram is equal to the product of its base and its altitude.

Download GGB File

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

Rectangle with Constant Perimeter

Move the dot on Slider A. What do you observe?

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The Pantograph

A pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen.

If a line drawing is traced by the first point, an identical, enlarged or miniaturized copy will be drawn by a pen fixed to the other. The pantograph was invented by Cristoph Scheiner.

Visualizing Multiplication of Fractions

Drag slider m to determine the fraction m/10 and drag sliders n to determine the fraction n/10. The area of the overlapping rectangles is the product of the fraction.


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

Download GGB File

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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