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What shape do you get when you join the mid-points of adjacent sides of a quadrilateral? Can you explain why this is or prove your results? What happens if you repeat the process one or more times?
In this activity students are able to carry out this investigation on Geometry page on their TI-Nspire. They can either use a tns file which provides five pre-drawn shapes, or start from scratch with a blank document.
There is a 2-page student handout that includes instructions on how to carry out the basic constructions if using the tns file.
Included in the teacher notes are ""What is a semigram?"" and a rationale for doing this activity.