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Constructions of Isosceles and Equilateral Triangles

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Students will discuss the difference between drawing and constructing a triangle using The Geometerís 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:

  • The angles opposite the congruent sides of an isosceles triangle are also congruent.

  • The three interior angles of an equilateral triangle are congruent.

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.

The following sketch illustrates the constructions of an isosceles and of an equilateral triangle.




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Last modified on August 13, 2001.