GEOMETRYCharacter builds slowly, but it can be torn down with incredible swiftness.
Faith Baldwin
Today:10.3 InstructionPractice
Character builds slowly, but it can be torn down with incredible swiftness.
Faith Baldwin
Assignment:10.2 p 710 #7-9, 44-47, 59, 63-64
GEOMETRY
10.3 - ARCS AND CHORDS
Objectives: Know and use relationships between arcs
and chords Know and use properties of chords of
circles
Vocabulary: congruent arcs
Content Standards
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords.
G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Mathematical Practices
4 Model with mathematics.
3 Construct viable arguments and critique the reasoning of others.
You used the relationships between arcs and angles to find measures.
• Recognize and use relationships between arcs and chords.
• Recognize and use relationships between arcs, chords, and diameters.
central angle
minor arc – connects an angle under 180°
major arc –
connects an angle over 180°
Named by two letters
Named by three letters
B
C
A
D
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
ABCD if and only if ABCD
A
B
C
D
If a diameter or radius of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
DEEF, DGGF
F
G
E
D
OIf OG is a diameter of circle O, then
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
A
F
C
BABCD if and only if EFEG
D
G
What happens if the segment is also perpendicular?
Use a Diameter Perpendicular to a Chord
CERAMIC TILE In the ceramic stepping stone
below, diameter AB is 18 inches long and chord EF
is 8 inches long. Find CD.
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