We learned about bisecting angles and perpendicular bisectors through creating Mandalas.
To begin, all that's needed is a good quality compass, paper and a straight edge (like a ruler). There is an endless possibility of mandalas that can be created. We have a book of simple geometric mandalas and find it very educational to try to recreate them. Interestingly enough, there usually ends up being more than one way each mandala can be created. In other words, sometimes steps can proceed in different orders, or alternative steps can be used which arrive at the same result. After walking kids step-by-step through the creation of several mandalas, I like to give them a challenge mandala and see if they can create one on their own.
Each mandala created requires some construction lines which end up being erased in the final version. Therefore, it's best to draw them lightly. Here are the steps we used to create the above mandala.