Geometry

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

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

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

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

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)

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

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

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

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

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!

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