6.1.1 Understand and use angle properties (3)

This week's tasks continue the **angle chasing** theme, and where again it might help to add auxiliary lines or to
transform part of the given figure, for example by a translation or
rotation. However, the context no longer involves regular polygons.

**Monday**: Here we need to use the fact that the brown line segments are parallel. It may take a while for students to spot a way of doing this, as the parallel lines are not connected in the usual, simple way, by a transversal.

The task can be solved in a rich variety of ways. Here are some of the methods that were posted on Twitter:

The above methods all involve auxiliary lines. It is also possible to solve the task using transformations, for example a rotation, as here, where the parallel lines become orthogonal:

**Tuesday**: This task involves a lot of redundant information. It can be made much simpler by, for example, translating the lowest two segments in the diagram such that the purple segments touch or overlap.

**Wednesday**: Here the redundant part of the diagram in Tuesday's task has been erased. This might help students who struggled with the task to find a solution.

**Thursday**: This is a classic task that I am particularly fond of (see here). It can be solved in a variety of ways, by adding an auxiliary line or by transforming part of the figure.

Here is an elegant, and perhaps the most common, way of solving the task:

**Friday**: This is, in essence, a very simple variant of Thursday's task: it is of exactly the same form, but with angle

*a*moved to a rather awkward and unorthodox position.

As in the previous task, the size of *a* is the sum of the two given angles: