geometry spring semester final review – unit 11 – circles...

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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