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Constructions
of Isosceles and Equilateral Triangles


 
Students will discuss the difference
between drawing and constructing a triangle using The
Geometer’s Sketchpad. They
will further develop constructions for both isosceles and equilateral
triangles. In the extension
activities, students will script their construction of a right triangle.
Mathematics:
The students will develop
constructions for an isosceles and an equilateral triangle. Students will
conjecture the following theorems:
Extension activities include: (1) Proving Euclid's first
proposition in the Elements,
"For a line segment AB, there is an equilateral triangle having the
segment as one of its sides" and (2) Developing a construction for a
right triangle. Mathematical
Thinking:
In this
activity, students will be asked to conjecture and prove
the aforementioned theorems and proposition.
They will also use critical thinking skills to develop their constructions for an
isosceles and for an equilateral triangle. Technology:
This activity (with its extensions)
uses several Sketchpad commands such as: Circle By Center +
Radius, Point on Object, Length, measure an
Angle, Point of Intersection,
Hide Objects, Perpendicular Line, Save As, Select All, Script and Make
Script. 

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