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Angle

ALL trig ratios in one place

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Trigonometric Identities Reference Angle Measures Basic Trigonometry Ratios Pythagorean Theorems Quotient Identities Reciprocal Identities 180?
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Prove Lines Are Parallel

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#OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY?? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? ? ?? ??? 6/#!"5,!29 0ARAGRAPH?PROOF????????v?V>??Li??????i????? ?>?>}?>???v???]?V>??i`?>??>?>}?>???????v? 0/345,!4%???? ? ?#/22%30/.$).'?!.',%3? #/.6%23% )F?TWO?LINES?ARE?CUT?BY?A?TRANSVERSAL? ? ? ? ? ? SO?THE?CORRESPONDING?ANGLES?ARE?? CONGRUENT??THEN?THE?LINES?ARE?? ? ?>?>??i??? &IND?THE?VALUE?OF?X?THAT?MAKES?MIN?? ? ? ??? ????????? 3OLUTION ,INES?M?AND?N?ARE?PARALLEL?IF?THE?? MARKED?CORRESPONDING?ANGLES?? ARE?CONGRUENT? ??X???? ????? ???? ?? 5SE?0OSTULATE????TO?WRITE?AN?EQUATION? ? ?X???? ?n?? 3UBTRACT?? ???FROM?EACH?SIDE? ? X???? ?{?? $IVIDE?EACH?SIDE?BY?? ?? ? 4HE?LINES?M?AND?N?ARE?PARALLEL?WHEN?X???? ?{?? %XAMPLE??? !PPLY?THE?#ORRESPONDING?!NGLES?#ONVERSE ? ???

Use Parallel Lines and Transversals

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??? ? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? #OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY? 0/345,!4%???? ? ?#/22%30/.$).'?!.',%3? 0/345,!4% )F?TWO?PARALLEL?LINES?ARE?CUT??? ? ? ? ? ? ? BY?A?TRANSVERSAL??THEN?THE?PAIRS?? OF?CORRESPONDING?ANGLES?ARE?? ? V??}??i??? ? 4HE?MEASURE?OF?THREE?OF?THE?NUMBERED?? ? ? ? ???? ? ? ? ? ? ANGLES?IS???????)DENTIFY?THE?ANGLES??? %XPLAIN?YOUR?REASONING? 3OLUTION "Y?THE?#ORRESPONDING?!NGLES?0OSTULATE??? ? ???? ????????? 5SING?THE?6ERTICAL?!NGLES?#ONGRUENCE?4HEOREM??? ? ???? ????????? "ECAUSE????AND????ARE?CORRESPONDING?ANGLES??BY?THE?? ? ???i????`??}???}?i??*?????>?i? ??YOU?KNOW? THAT?? ??x? ????????? %XAMPLE??? )DENTIFY?CONGRUENT?ANGLES ? ??? )F?M??????????FIND?M????M?????? ?? ? ? ? ? ? ? ? AND?M????4ELL?WHICH?POSTULATE?OR??

Identify Pairs of Lines and Angles

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??? ? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? #OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY? ??? )DENTIFY?0AIRS?OF?,INES?AND? !NGLES 'OAL? +??)DENTIFY?ANGLE?PAIRS?FORMED?BY?THREE?INTERSECTING? LINES? 6/#!"5,!29 0ARALLEL?LINES??/??????i??>?i??>?>??i?????i???v???i??`?? ???????i??iV??>?`?>?i?V???>?>?? 3KEW?LINES?/??????i??>?i???i?????i???v???i??`?????? ???i??iV??>?`?>?i?????V???>?>?? 0ARALLEL?PLANES??/?????>?i????>??`?????????i??iV??>?i? ?>?>??i????>?i?? 4RANSVERSAL??????>???i??>?????>????i???>?????i??iV??? ??????????i?V???>?>?????i??>??`?vvi?i?????????? #ORRESPONDING?ANGLES??/???>?}?i??>?i?V???i????`??}? >?}?i???v???i???>?i?V???i????`??}??????????? !LTERNATE?INTERIOR?ANGLES??/???>?}?i??>?i?>??i??>?i? ???i?????>?}?i???v???i????i?Li??ii????i????????i??>?`?

Prove Angle Pair Relationships

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??? ? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? #OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY? ??? 0ROVE?!NGLE?0AIR?2ELATIONSHIPS 'OAL? +?5SE?PROPERTIES?OF?SPECIAL?PAIRS?OF?ANGLES? 4(%/2%-????? ? ?2)'(4?!.',%3?#/.'25%.#%? 4(%/2%- !LL?RIGHT?ANGLES?ARE?? V??}??i??? ? 4(%/2%-????? ? ?#/.'25%.4?3500,%-%.43? 4(%/2%- )F?TWO?ANGLES?ARE?SUPPLEMENTARY?TO?THE?? ? ? ? ? SAME?ANGLE??OR?TO?CONGRUENT?ANGLES ??? THEN?THEY?ARE?? V??}??i??? ? )F????AND????ARE?SUPPLEMENTARY?AND????AND????? ARE?SUPPLEMENTARY??THEN?????????? ? 4(%/2%-????? ? ?#/.'25%.4?#/-0,%-%.43? 4(%/2%- )F?TWO?ANGLES?ARE?COMPLEMENTARY?TO?THE?? ? ? ? ? SAME?ANGLE??OR?TO?CONGRUENT?ANGLES ??? THEN?THEY?ARE?? V??}??i??? ? )F????AND????ARE?COMPLEMENTARY?AND????AND????ARE? COMPLEMENTARY??THEN???{?????? ?

Proving Cyclic Quadrilateral Rules

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A Development of Proof Through Cyclic Quadrilaterals Developed by Kimberly Aitken This lesson was developed for use in a geometry class as a stepping stone towards the mastery of proof writing skills. It incorporates knowledge on the geometry of circles as well as angles, and it provides students with additional exposure beyond the curriculum on writing proofs.

Geometry

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GRADUATE RECORD EXAMINATIONS? Math Review Chapter 3: Geometry Copyright ? 2010 by Educational Testing Service. All rights reserved. ETS, the ETS logo, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries. ?

Geometry

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GRADUATE RECORD EXAMINATIONS? Math Review Chapter 3: Geometry Copyright ? 2010 by Educational Testing Service. All rights reserved. ETS, the ETS logo, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries. ?
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