Geometry Spring Semester Final Review – Unit 11 – Circles 2016 1 Topics Covered in Unit 11 are Measuring Angles and Arcs, Arcs and Chords, Inscribed Angles, Tangents, Constructing Circumscribed and Inscribed Figures, and Secants, Tangent, and Angle Measures. Vocabulary/Formulas from Unit: Terms/Formula Name Description/Formula Figure/Drawing Sum of Central Angles ! < ! + ! < ! + ! < ! = !"#° Minor Arc The shortest arc connecting two endpoints on a circle. ! !" = ! < !"# = ! Major Arc The longest arc connecting two endpoints on a circle. ! !"# = !"#° − ! !" = !"#° − ! Semicircle An arc with endpoints that lie on a diameter. ! !"# = !"#° Arc Length ! = ! !"# ∗ !"# Theorem about Arcs and Chords !" ≅ !" !" !"# !"#$ !" !" ≅ !". Perpendicular Chord with Radius or Diameter !" !" !" !"#!"#$%&’()* !" !"#$% !" , !"#$ !" ≅ !" !"# !" ≅ !" . Perpendicular Chord with Radius or Diameter !" !" !" ! !"#!"$%&’()*# !"#$%&’( !" !"#$% !" , !"#$ !" !" ! !"!"#$#% !" ⊙ !.
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Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Topics Covered in Unit 11 are Measuring Angles and Arcs, Arcs and Chords, Inscribed Angles, Tangents, Constructing Circumscribed and Inscribed Figures, and Secants, Tangent, and Angle Measures. Vocabulary/Formulas from Unit:
Terms/Formula Name
Description/Formula Figure/Drawing
Sum of Central Angles
! < !+! < !+! < ! = !"#°
Minor Arc
The shortest arc connecting two endpoints on a circle.
!!!"! =! < !"# = !
Major Arc
The longest arc connecting two endpoints on a circle.
!!!"#! = !"#°−!!!"! = !"#°− !
Semicircle
An arc with endpoints that lie on a diameter.
!!!"#! = !"#°
Arc Length ! = !
!"# ∗ !"#
Theorem about Arcs and Chords
!" ≅ !"!!"!!"#!!"#$!!"!!" ≅ !".
Perpendicular Chord with Radius or Diameter
!"!!"!!"!!"#!"#$%&'()*!!"!!"#$%!!",
!!"#$!!" ≅ !"!!"#!!" ≅ !".
Perpendicular Chord with Radius or Diameter
!"!!"!!"!!!!"#!"$%&'()*#!!"#$%&'(!!"!
!"#$%!!", !"#$!!"!!"!!!!"!"#$#%!!"!⊙ !.
Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Perpendicular to Chords
!" = !"!!"!!"#!!"#$!!"!!" ≅ !".
Inscribed Angle Theorem ! < ! = !
!!!"
!!" = !" < !
Inscribed Angles to the same Arc
< !!!"# < !!!"#$!!"#$%&$'#!!!.!
!" < ! ≅< !.
Triangle with Diameter as a side.
!"!!"#!"!!!!"#$%$&%'", !"#$!
! < ! = !"°. !"!! < ! = !"°, !"#$!!"#!!"! !!!"#$%$&%'"!!"#!!"!!"!!!!"#$%&%'.
Quadrilateral Inscribed in Circle
!"!!"#$%&'#()%#'!!"#$!!"!!"#$%!&'(! !"!⊙ !, !"#$ < !!!"# < !!!"#!!
!""#$%$&'()*!!"# < !!!"# < !!!"#!! !""#$%$&'()*.
Tangent Theorem
!"#$!!!!"!!"#$%#!!!"!⊙ !!!!!!"#!!"#$!!"! !! ⊥ !".
Two Tangents Theorem
!"!!"!!"#!!"!!"#!!"#$%#!!!"!⊙!,!
!"#$!!" ≅ !".
Secants Intersecting Inside Circle Theorem
! < ! = !! !!"+!!"
! < ! = !! (!!"+!!")
Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Angle on Circle Theorem
! < ! = !!!!"
! < ! = !!!!"#
Two Secants Theorem
! < ! = !! (!!"−!!")
Secant and Tangent Theorem
! < ! = !! (!!"−!!")
Two Tangents Theorem
! < ! = !! !!"#−!!"
! < !+!!" = !"#°
Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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Geometry Spring Semester Final Review – Unit 11 – Circles 2016
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