4 3a Central and Inscribed angles by s3dn6csQ

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									      4.3a: Central/Inscribed Angles
                in Circles
                               p. 452 -458



    GSE’s
  Primary
M(G&M)–10–2 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).
Central Angle: an angle whose vertex is at the center of the circle
                              A
Circle B
                                      ABC         Has a vertex at the center

                 B



                                  C

Sum of Central Angles: The sum of all central angles in a circle
                       Is 360 degrees.
                      A

                                      Find m ADC
                 80
             B
     D

                                      Little m indicates degree measure of the arc
                          C
AC is a minor arc. Minor arcs are less than 180 degrees. They use the
 the two endpoints.



ADC is a major arc. Major arc are greater than 180 degrees. They use
three letters, the endpoints and a point in-between them.
Major Concept: Degree measures of arcs are the same as its central angles




                                           What is the mFY?


                                          What is the mFRY?
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
                In Circle P
m1  140 with diameter AC. Find each measure.
1) m2
     
2) m BC
     
     
3) m AB

4) m ABC
5) mPAB
In circle F, m  EFD = 4x+6, m  DFB = 2x + 20. Find mAB
NECAP Released Item 2009
Inscribed Angle: An angle with a vertex ON the circle and made up of 2 chords

                                ABC Is the inscribed angle




Intercepted Arc: The arc formed by connecting the two endpoints
                 of the inscribed angle
Major Concept:

Inscribed angles degree measures are half the degree measure of
 their intercepted arc

Ex

                                 What is mACB
What is the mBG




 What is the mGCB?
Major Concept:   If 2 different inscribed angles intercept the same arc, then
                 the angles are congruent



                                 find mACB
                                 and mAGB
Important Fact: If a quadrilateral is inscribed in a circle, then the opposite angles
                  are SUPPLEMENTARY




                                                        What angles are supplementary
Example:
           Circle C, mS  28 and mR  110
                   Find mQ and mT
Find the degree measure
of all angles and arcs
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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