Today in Geometry I asked students to draw a line then create another parallel to it.

There were a lot of crazy constructions.

Some students drew a line then used the opposite side of the straight edge to construct a parallel line. Others copied angles or used an insane amount of circles. Here’s one of those methods:

*Students were using a straight edge and compass

*Start with a line segment*

*Construct a circle whose radius spans more than half the segment.*

*Copy that same circle, this time centered and the other endpoint. ***(they just made a perpendicular bisector…)**

*Copy the same circle again, but make it just touch point B and do the same for the A side also.*

*Connect the first intersection of the circles to the third.*

There are a few points that I am uneasy with here but this particular student created a parallel line; doing exactly what they were asked to do. They also created an isosceles trapezoid, which is pretty awesome.

Here is the big question… if this method were used on a test would you mark it correct?

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Yes, because it is correct. I found students doing this as well. The challenge comes when you ask them to construct a parallel through a defined point. That tends to drive them toward some of the more traditional approaches, and it is often the first time they really get that two perpendiculars can make a parallel:)

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I held back from commenting on their different approaches. We are construction a parallel through a point today, it will be interesting to see how students modify their constructions! Thanks for stopping by!

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