Download Geometry Notes G.11 (10.2 10.3) Circles: Arc Measures, Chords Mrs

Geometry Notes G.11 (10.2 10.3) Circles: Arc Measures, Chords
Mrs. Grieser
Name: _______________________________ Date: _____________ Block: _______
Definitions
Central angle
Minor arc
Major arc
Semicircle
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
Angle whose vertex is the center of a circle.
Part of a circle that measures less than 180o
Part of a circle that measures between 180o and 360o
Arc with endpoints that are the endpoints of a diameter; measure is 180o
Minor arcs are named by their endpoints; example:
Major arcs and semicircles are named by endpoints and a point on the arc;
example:





Write “measure of arc AB” as: m
The degree measure of an arc is the measure of its central angle
The measure of an arc formed by two adjacent arcs is the sum of the
measures of the two arcs
Circles are congruent if they have the same radius measure
Arcs are congruent if they have the same measure and are arcs of the
same or congruent circles
Example: Find the measures of each arc of
P, where
is the diameter.
You try…
1) Find the measures of
J, where KM is a diameter.
2) Identify the given arc as a major arc, minor arc, or semicircle, then find the measure
of the arc.
3) Tell whether the highlighted arcs are congruent.
a)
b)
d)
c)
e)
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Geometry Notes G.11 (10.2 10.3) Circles: Arc Measures, Chords
Mrs. Grieser
Chord Properties
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A chord is a segment with endpoints on a circle; divides the circle into two arcs
A chord through the center of a circle is a diameter; divides the circle into two semicircles
Theorem
In the same or congruent circles, two minor arcs are
congruent IFF their corresponding chords are congruent.
Theorem
If one chord is a perpendicular bisector of another chord,
then the first chord is a diameter.
Theorem
If a diameter of a circle is perpendicular to a chord, then
the diameter bisects the chord and its arc.
Theorem
In the same circle or congruent circles, two chords are
congruent IFF they are equidistant from the center.
Examples:
a) Given
D…
b) Find the
measure of:
c) Find the
measure of:
1) CU
2) QU
3) radius of
C
You try…
a) Given the circles are congruent,
b) Find BD
e) Find EF
and the
radius of
the circle
f) In the diagram for question
e), suppose AB = 27 and EF =
GF = 7. Find CD.
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