Day 3 –
Using Chords of Circles
A
point Y is called the midpoint of Arc XYZ if Arc XY 
Arc YZ. Any line, segment,
or ray that contains Y bisects Arc XYZ.
THEOREMS
ABOUT CHORDS OF CIRCLES:
1st Theorem:
In the same circle, or in congruent
circles,
two minor arcs
are congruent if and only if
their
corresponding chords are congruent.
Proof: We
have 2 different cases involved in this proof.
The first is when two minor arcs are in the same circle. The second case involves the chords being in
congruent circles.
CASE I: Two chords In Same Circle
In CASE II, our proof will look much like above,
however, we will be dealing with 2 congruent circles versus the same
circle. Therefore, we’ll need to Use the
Definition of Congruent Circles and our Transitive Property.
2nd
Theorem:
If a
diameter of a circle is perpendicular to a chord,
then the
diameter bisects the chord and its arc.
Proof:
3RD
Theorem:
If one chord
is a perpendicular bisector of
another chord, then the first chord is a diameter.
Proof:
4TH
Theorem:
In the same circle, or in congruent
circles,
two chords are
congruent if and only if they are
equidistant from the
center.
Proof:
