4.3a: Angles and Arcs

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4.3a Angles and Arcs

• p. 452 -458

GSEs
Primary
M(GM)102 Makes and defends conjectures,
constructs geometric arguments, uses geometric
properties, or uses theorems to solve problems
involving angles, lines, polygons, circles, or
right triangle ratios (sine, cosine, tangent)
within mathematics or across disciplines or
contexts (e.g., Pythagorean Theorem, Triangle
Inequality Theorem).
2
Central Angle an angle whose vertex is at the
center of the circle
A
Circle B
Has a vertex at the ________
B
C
Sum of Central Angles
A
Find m
80
B
D
Little m indicates ________ measure of the arc
C
3
AC is a ___________. Minor arcs are ________ than
180 degrees. They use the the two endpoints.
ADC is a ____________. Major arc are ___________
180 degrees. They use three letters, the
endpoints and a point in-between them.
4
Major Concept Degree measures of arcs are the
same as its _________________
What is the mFY?
What is the mFRY?
5
Circle P has a diameter added to its figure every
step so all central angles are congruent. What
is the sum of the measures of 3 central angles
after the 5th step? Explain in words how you
know.
Step 2
Step 1
Step 3
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Concentric Circles- circles with the same center,
but different Radii
What is an example you can think of outside of
geometry?
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In Circle P
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Arc Length
Would we have enough info to find the
circumference?
What would be needed?
Lets assume the radius of the circle is 4 inches.
Can we find the circumference now?
What if we just want to know the distance of the
circumference from A to C?
What would make sense as an approach to find the
length?
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Find the length of BC
Find the length of CFB
What relationship should they have for this
problem?
What is mCFB ?
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In circle F, m EFD 4x6, m DFB 2x
20. Find mAB
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NECAP Released Item 2009
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An angle with a vertex ______ the circle and made
up of 2 chords
Inscribed Angle
Is the inscribed angle
The arc formed by ________________________________
_____ of the inscribed angle
Intercepted Arc
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Major Concept Inscribed angles degree measures
are ______________________ measure of their
intercepted arc
Ex
What is
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What is the mBG
What is the mGCB?
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If 2 different inscribed angles intercept the
same arc, then the angles are __________________
Major Concept
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Important Fact If a quadrilateral is inscribed
in a circle, then the opposite angles
are _______________
What angles are supplementary
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Example
Circle C,
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Find the degree measure of all angles and arcs
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