2011 - 2012 Learning Standards for Geometry

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10 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Battle Ground

Public Schools


May, 2012



2011
-

2012

Learning Standards for
Geometry


Logical Arguments and Proofs




Distinguish between inductive and deductive reasoning.
(10
.1
.a
)



Use inductive reasoning to make conjectures, to test the plausibility of a geometric stateme
nt,
and to help find a counterexample.
(10
.1
.b
)



Use deductive reasoning to prove that a valid geometric statement is true.
(10
.1
.c
)



Write the converse, inverse, and contrapositive of a valid proposition and determine their
validity.
(10
.1.d
)



Identify

errors or gaps in a mathematical argument and develop counterexamples

to refute
invalid statements about geometric relationships.
(10
.1.e
)



Distinguish between definitions and undefined geometric terms and explain the role of
definitions, undefined terms
, postulates (axioms), and theorems.

(10
.1.f
)



Lines and Angles




Know, prove, and apply theorems about parallel and perpendicular lines.

(10
.2
.a
)



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楮ie牳rc瑥t

by a⁴牡湳癥牳a氮l
⠱(


)



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灥牰r湤楣畬n爠汩湥献s
⠱(


)



䑥獣物扥⁴ e⁩湴e牳rc瑩潮猠潦楮敳⁩渠o桥⁰污湥⁡湤⁩渠獰aceⰠ潦楮敳⁡湤⁰na湥猬⁡湤n⁰污 e猠楮s
獰sc
e⸠
⠱(
⸲⹤
)


Two
-

and Three
-
Dimensional Figures




Know, explain, and apply basic postulates and theorems about triangles and the special lines, line
segments, and rays associated with a triangle.
(
10.3
.a
)



䑥瑥t浩湥⁡湤⁰牯癥⁴物 湧汥lc潮g牵rnceⰠ瑲楡ngl
e⁳業楬a物ryⰠa湤

潴桥o⁰牯灥牴楥s

of triangles.
(
10.3
.b
)



啳U⁴桥⁰
牯灥牴楥猠潦⁳灥c楡氠物i桴⁴物
angle猠⠳グ

60°

90° and
45°

45°

90°) to solve problems.
(
10.3
.c
)



䭮潷Ⱐ灲潶eⰠa湤⁡灰py⁴桥⁐y瑨tgo牥a渠周e潲om⁡湤⁩n猠s潮癥牳r.

(
㄰⸳

)



S潬癥⁰o潢汥浳

楮癯i癩vg⁴桥⁢a獩挠瑲sg潮潭整o楣i牡瑩潳映獩湥o⁣潳楮攬⁡湤⁴慮来湴⸠
(
㄰⸳

)



䭮潷Ⱐ灲潶eⰠa湤⁡灰py 扡獩挠瑨s潲o浳⁡扯畴⁰ara汬e汯lra浳⸠
(
㄰⸳

)



䭮潷Ⱐ灲潶eⰠa湤⁡灰py⁴桥潲o浳⁡扯畴⁰牯me牴楥s映煵a摲楬d瑥ta汳⁡湤瑨e爠灯ry杯湳n

(
㄰⸳

)



䭮潷
Ⱐ灲潶eⰠa湤⁡灰py 扡獩挠瑨s潲o浳⁲e污瑩lg⁣楲i汥猠瑯⁴ange湴猬⁣桯n摳d⁲ 摩dⰠ獥ca湴猬⁡湤n
楮獣i楢敤⁡ng汥献l
(
㄰⸳

)



䕸灬慩渠p湤⁰n牦潲洠o潮獴牵s瑩潮猠牥污瑥搠瑯⁴桥⁣楲i汥⸠
(
㄰⸳

)



䑥s
c物扥⁰物獭rⰠ,yra浩摳Ⱐ灡牡汬e汥灩灥摳Ⱐdet牡he摲dⰠ,湤n牥g畬ur

灯pyhed牡⁩渠 e牭猠潦⁴桥楲
晡ce猬sedge猬⁶s牴楣e猬⁡n搠灲d灥牴楥
s
⸠

㄰⸳

)



䅮Alyze c牯獳
-
獥c瑩潮猠潦⁣畢u猬⁰物獭猬⁰y牡浩d猬⁡湤⁳灨n牥猠a湤⁩摥湴楦y 瑨攠te獵汴楮i⁳桡pe献

(
㄰⸳

)


Geometry in the Coordinate Plane




Determine the equation of a lin
e in

the coordinate plane that is described geometrically,
including a line through two given points, a line through a given point parallel to a given line,
and a line through a given point perpendicular to a given line
.
(
10
.4
.a
)



Determine the coordinate
s of a point that is described geometrically
.
(10.4
.b
)



Verify and apply properties of triangles and quadrilaterals in the coordinate plane
.
(10.4
.c
)



Determine t
he equation of a circle
described geometrically in the coordinate plane and, given
equations

for a circle and a line, determine the coordinates of their intersection(s).

(10.4
.d
)

Battle Ground

Public Schools


May, 2012


Geometric Transformations




Sketch results of transformations and compositions of transformations for a given two
-
dimensional figure on the coordinate plane, and descr
ibe the rule(s) for performing
translations or for performing reflections about the coordinate axes or the line y = x
. (10.5.
a
)



䑥瑥t浩湥⁡湤na
灰py⁰牯灥牴楥猠潦⁴sa湳景f浡瑩潮m†⠱〮㔮
b
)



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Ⱐ,e獣物扥 a⁣o浰潳楴楯渠潦i
瑲t湳污瑩潮nⰠ牥晬fc瑩潮猬⁲潴o瑩潮猬⁡湤⁤楬a瑩潮猠oha琠獵灥t業灯獥猠潮s⁦ gu牥渠瑨攠潴
桥爮†
⠱〮(⹣
)



䑥獣物扥⁴ e⁳y浭et物r猠潦⁴oo
-
摩de湳楯na氠晩g畲e猠s湤⁤n獣物扥⁴牡湳景f浡瑩潮猬⁩湣汵摩湧
牥晬fc瑩潮猠oc牯獳⁡ 湥 a湤n
牯瑡瑩潮猠o扯畴

a point. (10.5
.d
)


Additional Key Content




Derive and apply formulas for arc length a
nd area of a sector of a circle
. (
10.6.a
)



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潦⁴桥⁥a牴
栮h

⠱〮(⹢
)



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-
摩de湳
楯湡氠iig畲e猠瑯⁳潬癥⁰o潢汥浳⸠o
⠹⸱⹣
)



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a牥aⰠ癯汵,eⰠ,爠獵rface a牥a映瑷o
-

a湤⁴
h牥e
-
摩de湳楯na氠晩l畲e献†⠱〮㘮d
)



啳U⁤楦 e牥湴⁤ngree猠s映灲pc楳i潮⁩渠oea獵se浥m琬⁥t灬慩渠瑨攠pea獯渠景s⁵獩湧⁡⁣e牴r楮⁤eg牥e
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a灰牯p物r瑥

p牥c楳i潮⁦o爠a⁧楶e渠灵
牰潳r⸠.⠱〮(⹥
)



S潬癥⁰o潢汥浳⁩湶潬癩ng a獵牥浥湴mc潮癥牳楯湳⁷楴桩渠慮搠扥瑷te渠ny獴敭猬⁩湣汵摩湧
瑨潳攠楮癯t癩湧⁤ 物癥搠d湩n猬⁡湤⁡湡lyze⁳潬畴u潮猠楮⁴e牭猠潦⁲ a獯sa扬敮e獳映
獯汵s楯湳i
a湤⁡灰牯p物a瑥⁵湩瑳⸠
.〮㘮0
)


Reasoning, Pr
oblem Solv
ing and Communication




Analyze a problem situation and represent it mathematically
. (
10.7
.a
)



Se汥l琠慮搠t灰py⁳瑲 teg楥猠瑯⁳潬癥

灲潢汥m
s
⸠.
(
1〮0

)



䕶E汵慴l⁡⁰牯扬r洠景m⁲ea獯湡扬敮b獳Ⱐse物ry⁩ 猠scc畲ucyⰠ,湤⁩湴e牰re琠t桥⁳潬畴u潮⁩渠o桥
c潮瑥
x琠潦⁴桥物 楮慬⁰i潢汥o
⸠.
(
㄰⸷

)



䝥湥ra汩ze⁡⁳潬畴u潮⁳o牡瑥ty⁦ 爠r⁳楮g汥⁰l潢oe洠m漠o⁣污獳l⁲e污瑥搠灲db汥浳Ⱐl湤⁡灰py a
獴牡瑥gy⁦潲 a⁣污獳l 牥la瑥搠灲潢o
e浳⁴漠獯o癥⁳ ec楦楣⁰牯 le浳
⸠.
(
㄰⸷

)



Rea搠d湤⁩湴e牰re琠摩agra浳Ⱐm牡灨猬pan
搠瑥d琠捯湴t楮i湧⁴桥⁳y浢潬猬慮杵g来Ⱐ,湤nc潮癥湴n潮猠
潦o瑨敭t瑩cs
⸠.
(
㄰⸷

)



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爠a g楶敮⁡u摩敮de⁡湤⁰n牰潳r
⸠.
⠱〮(⹧.



Sy湴桥獩ne⁩湦潲浡瑩潮⁴漠摲o眠w潮c汵獩潮猠o湤⁥癡汵慴l⁴桥⁡rg畭
e
湴猠慮搠d潮o汵獩潮猠潦o
潴桥os
⸠
㄰⸷.g)



啳U⁩湤畣瑩癥⁲ea獯湩湧⁴漠浡步⁣潮橥c瑵牥猬⁡湤n畳u⁤ 摵d瑩癥⁲ea獯湩ng⁴漠灲o癥爠摩獰 潶o
c潮橥o瑵牥献s⠱〮(.g)

ⴭⴭⴭⴭⴭ-ⴭ-ⴭⴭⴭ-ⴭ-ⴭⴭⴭⴭⴭⴭⴭⴭ-ⴭ-ⴭⴭⴭ-ⴭ-ⴭ

S瑡瑥⁷ 扳楴e⁷楴栠數a浰me猺

桴h瀺p⽳/an
摡牤献潳灩⹫ㄲr睡⹵猯C潮瑥湴L楳iByG牡摥⹡s
灸p獵扪ec琽㜬偅t杬㴱㐦ca瑥g潲y=2


䅮潴桥爠re扳楴e⁷楴栠 a瑨⁨敬瀺

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