Graphics Reference
In-Depth Information
a
b
h
c
Fig. 10.8.
A Right angled triangle.
Fig. 10.9.
The Theorem of Thales states that the right angle of a right triangle lies
on the circumcircle over the hypotenuse.
10.1.9 Theorem of Thales
Figure 10.9 illustrates the theorem of Thales, which states that the right angle
of a right triangle lies on the circumcircle over the hypotenuse.
10.1.10 Theorem of Pythagoras
Despite its name, there is substantial evidence to show that this theorem was
known by the Babylonians a millennium before Pythagoras. However, he is
credited with its proof. Figure 10.10 illustrates the well-known relationship
c
2
=
a
2
+
b
2
(10.11)
from which one can show that
sin
2
(
α
)+cos
2
(
α
) = 1
(10.12)
10.1.11 Quadrilaterals
Quadrilaterals
have four sides. Examples include the square, rectangle, trape-
zoid, parallelogram and rhombus, whose interior angles sum to 360
◦
.Asthe
square and rectangle are such familiar shapes, we will only consider the other
three.
