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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