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Teacher Notes

CONCEPT 1 - Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

1. The construction of an inscribed equilateral.

 TEACHER NOTE -- These reasons use concepts that have not been established yet. Most of them are concepts developed in G.C.2 where the basic angle and arc relationships in a circle are determined. I do think it is still important to get a sense of why things are working.

So why does this work?

2. The construction of an inscribed square.

So why does this work?

Reason #1 – A Square has diagonals that are perpendicular and congruent.  The perpendicular diameters determine the square.

Reason #2 – The perpendicular bisectors form a central angle of 90° which divide the circle into 4 congruent parts, thus forming the square.

3. The construction of an inscribed hexagon.

So why does this work?

Reason #1 – Step (D) divided the circle into six congruent arcs, thus six congruent chords.

Reason #2 – Step (D) created six equilateral triangles, ΔFAB. ΔBAG, ΔGAE, ΔEAC, ΔCAD, and ΔDAF) dividing the circle into six congruent parts.