Constructing triangles given the side lengths

Move AD, BE and CF to determine the side length of the triangle.

1 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

1.) Use the segment to construct the following triangles:
 a.) equilateral
 b.) scalene
 c.) isosceles
 d.) right

2.) Construct a triangle with side lengths 2, 2, and 4. What do you observe?
3.) Explain why your observations are such.

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The Parabola in Vertex Form

1. Move sliders a, h, and k. What do you observe? 
2. How are a, h, and k relates to the graph's movement? 
3. Make a generalization about the relationship between the parameters a, h, and k and the movement of the appearance of the graph.

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 parabola has vertex form .

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Rectangle-Triangle Area Relationship

Consider the rectangle and the triangle below.

1.  What do you observe? What are common properties between the two polygons?
2. Drag point D to change the height of the triangle and drag point A or B to change the length of the base. What do you observe?
3. What can you say about the areas of the two figures? Justify your answer. 
4. Click the Show Areas check box in the applet.  Was your answer in 3 correct? 
5. Drag point E. What is the relationship between the area of the rectangle and the area of a triangle? Explain why this is so. 

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 applet above demonstrates that the area of a triangle is half the area of a rectangle with the same base and height.

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