2011 - 2012 Learning Standards for Geometry

Ηλεκτρονική - Συσκευές

10 Οκτ 2013 (πριν από 4 χρόνια και 6 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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by a⁴牡湳癥牳a氮l
⠱(

)

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⠱(

)

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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

of triangles.
(
10.3
.b
)

angle猠⠳グ

60°

90° and
45°

45°

90°) to solve problems.
(
10.3
.c
)

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(
㄰⸳

)

S潬癥⁰o潢汥浳

(
㄰⸳

)

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

(
㄰⸳

)

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

s
⸠
㄰⸳

)

䅮Alyze c牯獳
-

(
㄰⸳

)

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

b
)

䝩癥渠瑷漠n潮g牵e湴⁯爠n業楬a爠r楧畲e猠楮⁡⁣潯牤o湡瑥⁰污湥
Ⱐ,e獣物扥 a⁣o浰潳楴楯渠潦i

⠱〮(⹣
)

䑥獣物扥⁴ e⁳y浭et物r猠潦⁴oo
-

a point. (10.5
.d
)

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

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⠱〮(⹢
)

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-

⠹⸱⹣
)

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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
-

)

a灰牯p物r瑥

p牥c楳i潮⁦o爠a⁧楶e渠灵

)

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)

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

s
⸠.
(
1〮0

)

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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

e浳⁴漠獯o癥⁳ ec楦楣⁰牯 le浳
⸠.
(
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)

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⸠.
(
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)

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⸠.
⠱〮(⹧.

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e

⸠ ㄰⸷.g)

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

䅮潴桥爠re扳楴e⁷楴栠 a瑨⁨敬瀺