Just recently i showed my students the angle bisector and perpendicular bisector constructions and we discussed why they worked. I allowed them some time to attempt the constructions themselves and as i walked around to help students with using the equipment i noticed a lot of mistakes. I recreated these mistakes and have put them into a ppt so that the class can discuss what is wrong about each construction.
Most of the mistakes made in the constructions were quite easy to spot but the one below right was harder. They eventually saw it was the two arcs that were constructed from the incorrect place that made the bisect wrong.
After looking at these errors i gave the students the following questions
The idea with these questions was to get students to think first about what letter they thought the bisector would pass through before they attempted the construction. This was because many of the students didn’t pay attention to whether their answer was sensible. I saw constructions where it was very obvious to the naked eye that the bisector wasn’t where they drew it. It also made it easy to get a rough idea of if the class could get the construction right by the simple fact the line should go through B. Obviously this doesn’t mean they definitely got it right but it was a start.
At the end of the lesson I gave the class the challenge of trying to construct a 45° angle
I let the students discuss it in pairs and i gave them a clue that you could do it with two constructions. With help they were able to arrive at the idea of bisecting the angle on a perpendicular bisector.