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Elements of Gothic windows in Geogebra

Elements of Gothic windows 

Hands on (3)

Circumcircle of a Triangle Construction

Construct the circumcircle of a triangle by following the construction steps below.  

Instructions

Select tool Polygon. Create an arbitrary triangle ABC by clicking three times in the Graphics View. Close the triangle by selecting the first point A again.

Activate tool Perpendicular Bisector.
Construct the Perpendicular Bisector for two of the edges of the triangle by successively selecting the segments.
Hint: You can find this tool in the Special Lines Toolbox (fourth Toolbox from the left).

Create intersection point D of the two the line bisectors.
Hint: Successively select the two line bisectors, or click directly on the intersection point.

Construct a circle with center D through one of the vertices of triangle ABC.
Hint: First, select point D, then, for example, point A.

Select the Move tool and drag the vertices of the triangle in order to check if your construction is correct.

Geogebra Physics Examples

Girl in the Mirror

Example to explore the question "How large does a mirror need to be to see your full body?" This problem can be used in connection with similar triangles.

Ann is 5 feet tall. She wants to hang a mirror so that when she stands 5 feet away from it she can see herself from her toes on the floor to the top of her head (6 inches above her eyes. How tall is the shortest mirror that she needs? Hint: Use the reflection tool. First reflect Ann about the line of the mirror. Then construct the segments from her eyes to the top of her head and the bottom of her feet. The mirror reflects the light from her head and feet to make it look like they are their “mirror image” behind the mirror. Does this fact let you prove that the “angle of incidence” (between the line from the eye to the mirror and the line of the mirror) is congruent to the “angle of reflection” (between the line from the foot to the mirror and the line of the mirror)?

Reflection and Refraction

 Explore the reflection and refraction of light.

Inclined Plane with Two Masses and a Pulley

This is a simulation showing two objects attached to each other with a massless string that passes over a pulley. One mass is on a frictionless surface. The angle of incline of this surface can be varied from zero degrees (horizontal surface) to ninety degrees where the device acts like an Atwood's machine.

Examples - animations in Geogebra

Geogebra More Examples

Symmetries

Rotations, reflections, translations

A triangle is rotated four times, then everything is reflected in the y-axis. Everything is translated along the vector.  

Author: Malin Christersson

Translation Symmetry

Axes of Symmetry

Find out about all the details in the Introduction to GeoGebra 4.2: http://www.geogebra.org/book/intro-en.pdf 

                

1. Drag point A with the mouse along the outline of the flower. What do you notice? Write down your observations. 

2. How many axes of symmetry does this flower have? 

Hint: Drag the green points in order to change the position of the line of reflection. Then, repeat step (1) for every position of the line. 
Hint: Click the little icon in the upper right corner in order to delete the traces.

3. Make a sketch of this worksheet including the flower and all lines of symmetry you were able to find.

Examples Geogebra

The construction in Geogebra showing the part Fickle Love of the French Garden in Villandry, France

The construction in Geogebra showing the part of the French Garden in Gruyeres, Switzerland