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Pentagon

Find the vertices of a pentagon given the midpoints of its sides.

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Triangle Mid Points

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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Pareq Exists

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

Three Tears

Stage: 4 Challenge Level: Challenge Level:1
This is initially an exercise in "de-construction" to enable construction.

The first calculation may involve a little algebra to rearrange the familiar area formula or substitution and solving the equation.
Either way it is necessary to establish the radius which will give the correct area.

Marking off the six arcs around a circle circumference is an important formative experience.

The student needs to check that they understand how this "works", how the process amounts to six equilateral triangles.