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i5° GEOMETRY.
A triangle is called a right-angled triangle when one angle
is 90 degrees ; the other two angles will then together consist of
90 degrees, because 90 -f 90 = 180. ( See Fig. 5).
An acute-angled triangle has all its angles acute. (See
Fig. 6).
Fig. 4.
Equilateral Triangle. Right-Angled Triangle. Acute Triangle.
The longest side in a right-angled triangle is called the
hypothenuse and the other two sides are called the base and
perpendicular. The square of the length of the hypothenuse is
equal to the sum of the squares of the lengths of the other two
sides. ( See Fig. 5).
a°- + b* = c-
2
From this law the third side of a right-angled triangle can
always be found, when the length of the other two sides is
known. Thus : ( See Fig. 5).
a = */ & b = Vc2 \Za2
+ b*
If, instead of the letters a, b, and c, numbers are used, for
instance, a = 3 and b = 4; what then is the length of c ?
c = */& + 4* a = Vo2 - 42
£ = V52 - 32
c = V9 + 10 a = \/ ’lo- 10 b = V25 — 9
c = \^1
Ih ci = \/9 b = VlT
c = 5 = 3 b = ±
A square is a plane figure having four right angles and
bounded by four straight lines of equal length. (See Fig. 7).
Fig. 7.
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