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Head First 2D Geometry by Dawn Griffiths, Stray

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finding missing angles
Angles can be made up of other, smaller angles
If you cut up an angle into pieces, the smaller angles
add up to the original angle.
+
=
BULLET
PA
TH
DOOR
MICKY
BENNY
FOOTPRINTS
BULLET FOUND
STUCK IN WALL HERE
18º
CRIME SCENE SKETCH
CASE GEO180
(ANGLES AS MEASURED
BUT DRAWING NOT TO
SCALE)
81º
86º
In the sketch,
this angle is made up
of these t
w
o, sma
ller
angles.
18º
PLAN VIEW
Angle Magnets
Which of these angles matches the mystery angle?
62º 72º 45º 67º
you are here 4 7
18º
…and this marking
come t
ogether to make this angle…
18º + 72º = 90º
or you could jus
t tes
t a
ll the magnets y
ou were
giv
en t
o find one that fits—making 90º.
angle magnets solution
Angle Magnets Solution
Which of these angles matches the mystery angle?
18º
62º 72º 45º
18º + ?º = 90º
18º
67º
means i
t’s a
r
ight angle = 90º.
We know that these tw
o angles
18º
72º
Y
ou could hav
e done 90–18 t
o find the 72º,
Q:
I checked that mystery angle with a protractor and it
wasn’t 72º—so how come you’re saying it is?
A:In geometry, unless you’re specifically told to measure
an angle, assume that the drawing isn’t accurate, but that the
numbers on the sketch are. We calculate missing angles rather
than measure them.
Q:
What about all the other lines on the diagram? Do we
know if they’re straight?
A:The other line segments on the sketch represent things
like walls or the path between two points. They’re all definitely
straight. In fact, the two line segments we’re interested in—the
bullet path and the path from Benny to Micky—are also straight.
What we need to find out is whether they join up to form one
single straight line.
Chapter 1 8

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