Relationships

1
Relationships between
ANGLES
ARCS

2
In chapter 2 the measure of arcs was always in
terms of absolute units like centimeters or
millimeters and dependent on the radius of the
circle. However, in chapter 3 the measure of
arcs will be in degrees, which is an indication
of a certain portion of a circumference (one full
circumference being 360º). This way of measuring
an arc is independent of the radius.
The 4 types of angles discussed earlier in the
course all have a special relationship with their
intercepted arc(s).
3
As far as central angles are concerned the
measure of the angle is equal to the measure of
the intercepted arc.
This means that if you know the measure of the
intercepted arc of a central angle, you can
determine the measure of the angle OR if you know
the measure of the central angle, you can
determine the measure of the intercepted arc.
THEOREM 14
4
THEOREM 15
5
The relationship that an inscribed angle has with
its intercepted arc is that the measure of the
angle is one-half the measure of the arc.
THEOREM 16
6
When dealing with an inscribed angle, it doesnt
matter where the vertex is on the circumference.
If the intercepted arc is the same, the angle
will also be the same.
7
THEOREM 17
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TIME for YOU to PRACTICE