1. Geometry

2. Unit outline: Geometry (last topic!)
This week:
Angles (worksheet)
Congruence (10A)
Similarity (10B)
Next week
Angles in a circle (21A)
Intersecting chords, tangents and secants (21B)
Cyclic quadrilaterals (21C)
The week after
Revision/catch up/write summary sheet
SAC (test): Wednesday 5th or Friday 7th November (see how we go for time)
After this: exam revision

3. Angles - reminders
A circle has 360 degrees (this is called an angle of revolution)
A semi-circle has 180 degrees (this is also a straight angle)
A right angle is 90 degrees (a quarter of a circle, marked with a small square in the corner)
The angles of a triangle add to 180 degrees

4. Types of angles Acute: less than 90 degrees Right: 90 degrees
Obtuse: between 90 and 180 degrees
Straight: 180 degrees
Reflex: between 180 and 360 degrees

5. Adjacent angles Adjacent angles are next to each other
They share a vertex (point) and line

6. Complementary and supplementary angles
Complementary angles add to 90 degrees, and therefore occur within a right angle
Supplementary angles add to 180 degrees, and therefore occur on a straight line
If we know one of the angles, we can figure out the other one!
The complement of ∠ABC is ∠CBD (∠ABC + ∠CBD = 90)
The supplement of ∠KHJ is ∠JHI (∠KHJ + ∠JHI = 180)

7. Vertically opposite angles
These occur when you have two lines that cross over each other
Vertically opposite angles are equal

8. Corresponding angles
When two lines are cut by a third line (called a transversal) corresponding angles are in corresponding positions (i.e. on the same side of the transversal and both above/ both below the pair of lines)
If the lines are parallel, the corresponding angles are equal

9. Alternate angles
When a transversal cuts through a pair of parallel lines, it also creates alternate angles
Alternate angles are equal

10. Co-interior angles
Co-interior angles add up to 180 degrees (they are supplementary)

11. Solving unknown angles
It can be helpful to draw or visualise a circle around the intersecting lines – as we know what angles are in a circle, this can help us figure out what we know and what we don’t know
Figure out what rules apply – are the angles complementary/ supplementary? Are they vertically opposite, corresponding, alternate or co-interior? How can we use this information?
Start from whichever is easiest and work your way around until you have found all the unknown angles – there can be many ways of solving these problems!

12. Worksheet
Complete the questions – we will do some of them together but you also need to challenge yourselves!
Once you have figured out what to do, the actual maths isn’t too tricky. It is just the thinking process that is difficult, and sometimes frustrating! So help each other to work it out.
It is tricky – you need to use some algebra skills too (undoing to find x for example)
The extension questions are hard, but try them out! I will upload videos on how to do these questions on the website this week