geometry: chapter 10 10.2: chords#2. image taken from: geometry. mcdougal littell: boston, 2007. p....
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GEOMETRY: Chapter 1010.2: Chords#2
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 664.
Theorem 10.4
In the same circle, or
in congruent circles,
two minor arcs are
congruent if and only
if their corresponding
chords are congruent.
Ex.1:
Answer:108o
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
oIn , , and =108 .
Find .
R AB CD mAB
mCD
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Bisecting Arcs
If , then the point Y, and any line,
segment, or ray that contains Y, bisects .
XY YZ
XYZ
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Theorem 10.5
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Theorem 10.6
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
Ex. 2: Three props are placed on a stage at points, P, Q, and R as shown. Describe how to find the location of a table so it is the same distance from each prop.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Ex. 2: Three props are placed on a stage at points, P, Q, and R as shown. Describe how to find the location of a table so it is the same distance from each prop.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 665.
Ex. 3:
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
Use the diagram of to find the length
of and . Tell what theorem you used.
C
BF
Ex. 3:
Answer: 10; Theorem 10.5
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
Use the diagram of to find the length
of and . Tell what theorem you used.
C
BF
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 666.
Theorem 10.7
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
Ex. 4:
Answer: 20Images taken from: Geometry. McDougal Littell: Boston, 2007. P.666.
In the diagram of , ,
2 6, and 3 1.Find .
P PV PW
QR x ST x QR
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