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Prove Lines Are Parallel

Subject: 
Geometry
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Elementary geometry
Transversal
Parallel
Angle
line

#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

Subject: 
Geometry
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Tags: 
Elementary geometry
Transversal
Parallel
Angle
Tetrahedron
line

??? ? ,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

Subject: 
Geometry
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Elementary geometry
Transversal
Perpendicular
Parallel
Angle
Tetrahedron
line

??? ? ,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??>?`?

Use Postulates and Diagrams

Subject: 
Geometry
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Tags: 
Elementary geometry
line
Plane
Perpendicular

#OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY?? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? ? ?? 9OUR?.OTES ??? 5SE?0OSTULATES?AND?$IAGRAMS 'OAL? +?5SE?POSTULATES?INVOLVING?POINTS??LINES??AND?PLANES? 6/#!"5,!29 ,INE?PERPENDICULAR?TO?A?PLANE???????i?????i??i?`?V??>?? ???>???>?i??v?>?`???????v???i????i????i??iV?????i???>?i? ???>???????>?`?????i??i?`?V??>?????i?i??????i??????i? ??>?i???>?????i??iV??????>????>???????? 0/).4??,).%??!.$?0,!.%?0/345,!4%3 0OSTULATE??? ?4HROUGH?ANY?TWO?POINTS?THERE?EXISTS?EXACTLY? ONE?? ???i? ? 0OSTULATE??? !?LINE?CONTAINS?AT?LEAST?TWO?? ??????? ? 0OSTULATE??? ?)F?TWO?LINES?INTERSECT??THEN?THEIR?INTERSECTION? IS?EXACTLY?? ??i??????? ? 0OSTULATE??? ?4HROUGH?ANY?THREE?? ???V?????i>?? ?POINTS? THERE?EXISTS?EXACTLY?ONE?PLANE?

6.2 Notes

Subject: 
Algebra
Rating: 
0
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Tags: 
geometry
Elementary geometry
Quadrilaterals
Analytic geometry
Orientation
Perpendicular
Slope
line
Trapezoid
Parallelogram
Rectangle
Parallel

Unit 6 ? Linear Functions ? Slopes of Parallel & Perpendicular Lines Example 1 Plot points A(-4, 0) and B(-2, 4) and connect them. Plot points C(0, -2) and D(3, 4) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Example 2 Plot points A(1, 4) and B(-2, 3) and connect them. Plot points C(-2, 5) and D(0, -1) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Parallel lines have ________________ slope. Perpendicular lines have slopes that are the ______________________ of each other. When you multiply the slopes of perpendicular lines together, the product will be ______.

Relations and Functions Final Review

Subject: 
Algebra
Rating: 
0
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Tags: 
Mathematics
Analytic geometry
Elementary mathematics
Elementary algebra
equations
Functions and mappings
Linear equation
Slope
line
Continuous function
Function
Bresenham's line algorithm

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 t (Min) 1 2 3 4 5 6 d (km) 1 2 3 4 5?1?2?3?4?5 x 1 2 3 4 5 ?1 ?2 ?3 ?4 ?5 y Relations and Functions Practice Questions 1. The following distance-time graph represents the distance (in kilometres) a person bicycled during a 50-min period. Describe a possible scenario. 2. The table of values shows the cost of movie tickets at a local theatre. Number of Tickets Cost ($) 1 12 2 24 3 36 4 48 (a) Is this a linear or non-linear relationship? Explain how you know. (b) Assign a variable to represent each quantity in the relation. Which variable is the dependent variable and which is the independent variable?

Cultural line in the sand essay

Subject: 
Human Geography
Rating: 
0
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Tags: 
line
in
the
Sand

A vernacular region is a region that people believe exists as part of their cultural identity. The southern part of the United States mainland is controversial on where it actually ends. Part of the reason why it is not a definite boundary is because the ?south? and the ?north? are vernacular regions. The south is becoming more and more like the north because people move here to have a more tropical lifestyle. When the population of northerners grows in the south, the culture will change.
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