Line segment AB is drawn in the plane. Where should point C be placed so that ABC is a right triangle? …so that it is an isosceles triangle? …so that it is obtuse? This activity will allow you to explore these questions.
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Use the Show/Hide Random Triangle buttons to place point C randomly in the plane. Drag point C to change the orientation of triangle ABC.
Use the other Show/Hide buttons to reveal various types of triangles such that AB is one of the sides. When shown, the path of the third vertex for these triangles will be displayed, and the third vertex can be moved along the paths. (NOTE: It is a good idea to Hide a particular type of triangle before using the Show button to display another type, as the drawing may become cluttered otherwise. When a Hide button is clicked, the triangle will disappear, but the path will remain.)
The Clear All button can be used to remove all triangles and paths from the screen.
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BEFORE using the Show/Hide buttons, try to answer the following questions. Then, use the applet to prove (or disprove) your conjectures.
- Where can point C occur so that ABC is a right triangle?
- Where can point C occur so that ABC is an isosceles triangle?
- Are you sure you've found all of the answers to the two questions above? How are you sure?
After using the Show/Hide buttons (the paths should remain on the screen), answer the following question.
- What type of triangle occurs at the intersection of two paths?
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