*CONTAINS AN INTERACTIVE APPLET. BEST READ ON A LAPTOP OR DESKTOP.*

When the Greeks were making their constructions, they knew how to construct a triangle with sidelengths 3, 4, and 5, say. However, if a Greek then wanted to construct the slightly different 3, 4, 6 triangle, they would have to start from scratch. With Geogebra software, modern students are able to overcome this limitation and complete one a single construction for all triangles.

Watch the animation and note how the sidelengths of the triangle change and the segments on the left grow and shrink. Then recreate the same effect using the Geogebra applet. When using the

*Segment with Given Length*and

*Circle with Center and Radius*tools, type in "

*f*," "

*g*," or "

*h*," depending on the length desired.