High School Level Glossary Geometry Glossary / Translation of Geometry terms based on the Coursework for Geometry Grades 9 to 12. Word-for-word glossaries are used for testing accommodations for ELL/LEP students Last Updated: 08/10/09 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234
THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY 12234 Education - P-16 Office of Elementary, Middle, Secondary, and Continuing Education and Office of Higher Education Office of Bilingual Education and Foreign Language Studies http://www.emsc.nysed.gov/biling/ THE UNIVERSITY OF THE STATE OF NEW YORK Regents of the University MERRYL H. TISCH, Chancellor, B.A., M.A., Ed.D.... New York MILTON L. COFIELD, Vice Chancellor, B.S., M.B.A., Ph.D.... Rochester ROBERT M. BENNETT, Chancellor Emeritus, B.A., M.S.... Tonawanda SAUL B. COHEN, B.A., M.A., Ph.D... New Rochelle JAMES C. DAWSON, A.A., B.A., M.S., Ph.D.... Plattsburgh ANTHONY S. BOTTAR, B.A., J.D.... Syracuse GERALDINE D. CHAPEY, B.A., M.A., Ed.D.... Belle Harbor HARRY PHILLIPS, 3rd, B.A., M.S.F.S.... Hartsdale JOSEPH E. BOWMAN, JR., B.A., M.L.S., M.A., M.Ed., Ed.D... Albany JAMES R. TALLON, JR., B.A., M.A.... Binghamton ROGER TILLES, B.A., J.D.... Great Neck KAREN BROOKS HOPKINS, B.A., M.F.A... Brooklyn CHARLES R. BENDIT, B.A.... Manhattan BETTY A. ROSA, B.A., M.S. in Ed., M.S. in Ed., M.Ed., Ed.D... Bronx LESTER W. YOUNG, JR., B.S., M.S., Ed. D.... Oakland Gardens CHRISTINE D. CEA, B.A., M.A., Ph.D.... Staten Island WADE S. NORWOOD, B.A.... Rochester Interim President of the University and Commissioner of Education CAROLE F. HUXLEY Senior Deputy Commissioner of Education, P 16 JOHANNA DUNCAN-POITIER Associate Commissioner for Curriculum and Instructional Support JEAN STEVENS Coordinator, Office of Bilingual Education and Foreign language Studies PEDRO J. RUIZ Acknowledgements: The New York State Education Department Glossaries for Language Learners were reviewed and updated during the 2008-2009 school year. We would like to thank in these efforts the New York State Education Department Language BETACs (Spanish, Asian and Haitian Bilingual Education Technical Assistance Centers), the NYS Office of Curriculum, Instruction and Instructional Technology; the New York City Department of Education Office of Language Learners, and the NYC Department of Education Translation and Interpretation Unit. The State Education Department does not discriminate on the basis of age, color, religion, creed, disability, marital status, veteran status, national origin, race, gender, genetic predisposition or carrier status, or sexual orientation in its educational programs, services and activities. Portions of this publication can be made available in a variety of formats, including brailed, large print or audio tape, upon request. Inquiries concerning this policy of nondiscrimination should be directed to the Department s Office for Diversity, Ethics, and Access, Room 530, Education Building, Albany, NY 12234.
Problem Solving 문제해결 AA triangle similarity AAA triangle similarity AAS triangle congruence additive property of equality algorithm apply ASA triangle congruence conjecture 추측 ( 하다 ) constraints construct discover dynamic geometry software explore generalization inductive reasoning justify parameters reason truth value valid argument 두각이같으면닮은삼각형임세각이같으면닮은삼각형임두각과한변이같은삼각형은합동임덧셈등식알고리듬적용하다, 계산하다두각과사이에있는한변이같은삼각형은합동임 제한, 구속, 압박 ~ 을작도하다, 구성하다발견하다, 깨닫다다이내믹기하학소프트웨어연구하다, 탐험하다일반화, 귀납귀납적추론정당화하다, 해명하다매개변수, 모수, 도움변수추론하다, 논리적으로생각하다진리값타당한논쟁 Reasoning and Proof 추론및증명 AA triangle similarity AAA triangle similarity AAS triangle congruence analytical proof angle addition postulate ASA triangle congruence axiom biconditional conclusion conditional statement T-7686 () 1 두각이같으면닮은삼각형임세각이같으면닮은삼각형임두각과한변이같은삼각형은합동임분석적증명추가공준각두각과사이에있는한변이같은삼각형은합동임공리, 원칙쌍조건문결론조건부명제
conjecture conjunction contradiction contrapositive of a statement converse of a statement counterexample deductive proof deductive reasoning definition disjunction dynamic geometry software equivalence relation Euclidean Parallel Postulate explain geometry 추측논리곱모순대치명제역명제반례연역적인증명연역법정의논리합다이내믹기하학소프트웨어동치관계유클리드의평행공준설명하다기하학 hypotenuse and leg triangle congruence 합동삼각형의빗변및다리 hypothesis indirect proof inductive reasoning inverse of a statement investigate justify logical equivalent negation paragraph proof parallel postulate(s) proof proof by contradiction proportional Pythagorean Theorem reason reflexive property of equality SAS triangle congruence T-7686 () 2 가정간접증명귀납적추론역명제조사하다, 연구하다정당화하다, 해명하다논리적동치부정문장으로증명평행공준증명모순을이용한증명비례항파타고라스의정의추론하다, 논리적으로생각하다등식의반사적성질 (a=a) 두변과한각이같은두삼각형은합동임
SAS Similarity Theorem SSS triangle congruence substitution property subtraction property of equality symmetric property of equality theorem transformational proof transitive property of equality truth value two-column proof undefined terms union of sets valid argument Communication 한각의크기가같고두변의비율이같은삼각형은닮은삼각형이된다는정리 세변의길이가같으면합동삼각형임 치환법칙 뺄셈의상등법칙 등식의대칭적성질 (a=b 이면 b=a) 정리 변형증명 등식의추론적성질 (a=b 이고 b=c 이면 a=c) 진리값 이열증명 정의를내리기힘든항 합집합 타당한논쟁 의사교환 axiom biconditional compound statement conclusion conditional statement 공리, 원칙상호조건적인복합명제결론조건부명제 conjecture 추측 ( 하다 ) conjunction contrapositive of a statement converse of a statement definition disjunction explain hypothesis inverse of a statement justify negation theorem truth value T-7686 () 3 논리곱대치명제역명제정의논리합설명하다가정역명제정당화하다, 해명하다부정정리진리값
undefined terms 정의를내리기힘든항 Connections 연결, 관계, 결합 apply compound locus discover intersection of sets investigate spatial relationships union of sets 적용하다, 계산하다복합궤적발견하다, 깨닫다교집합조사하다, 연구하다공간관계합집합 Representation analytical geometry coordinate geometry definition Euclidean geometry function graphical representation locus of points logical equivalence non-euclidean geometry three dimensional space transformational geometry two dimensional space Geometric Relationships AA triangle similarity AAA triangle similarity AAS triangle congruence ASA triangle congruence absolute value acute angle acute triangle adjacent angles 표현, 대표, 진술해석기하학좌표기하학정의유클리드의기하학함수, 기능, 작용표로표현궤적의점논리적동치비유클리드의기하학삼차원공간변형기하학이차원공간기하학적관계두각이같으면닮은삼각형임세각이같으면닮은삼각형임두각과한변이같은삼각형은합동임두각과사이에있는한변이같은삼각형은합동임절대값예각예각삼각형이웃각 T-7686 () 4
algebraic representation alternate interior angles altitude analytical geometry angle angle bisector angle measure apothem arc arc measure area axis of symmetry base betweeness bisector center of a circle center of a regular polygon center of gravity central angle central angle of a regular polygon centroid chord circle circumcenter 대수적표현엇내각높이해석기하학각각의이등분선각의측량변심거리호호의측량영역, 면적대칭축밑, 변, 기본사이성이등분선원의중심정다각형의중심중력, 중심중심각정다각형의중심각무게중심현원외심 circumcircle (about a polygon) 외접원 ( 다각형의 ) circumference collinear points common tangents complementary angles concave polygon concentric circles concurrent lines cone 원주공선점공통탄젠트보각오목다각형동심원공점선원뿔 T-7686 () 5
congruence conic sections constant of proportionality convex polygon coordinate geometry coplanar corresponding angles corresponding parts corresponding sides crossection cube cylinder definition diagonals diameter dihedral angle distance distance between a point and a line distance between two parallel lines distance between two points dodecahedron ellipse endpoint equiangular equidistant equilateral triangle equilateral polygon Euclidean Geometry Euclidean Parallel Postulate exterior exterior angle external secant segment face of a polyhedron 합동원뿔곡선상수비례볼록다각형좌표기하학동일편면상동위각대응부위동위변횡단면정육면체운기둥정의대각선지름이면각의거리점과선사이의거리두평행선사이의거리두점사이의거리 12면체타원말단, 끝등각의등거리의정삼각형정다각형유클리드의기하학유클리드의평행공준바깥쪽의외각외부활선선분다면체의한면 T-7686 () 6
foot of an altitude function geometric mean geometry golden ratio golden rectangle great circle hemisphere Heron's formula hexagon hypotenuse icosahedron incenter of a polygon inclination inscribed angle inscribed circle intercepted arc intercepts interior intersecting lines isosceles trapezoid isosceles triangle kite lateral area of a prism lateral edge lateral face lateral surface legs of a right triangle legs of an isosceles trapezoid length line line segment 수선의발 ( 삼각형의꼭지점에서대변에그은수직선이만나는점, perpendicular foot 이라고도함 ) 함수, 기능, 작용 기하학적평균 기하학 황금비율 황금비율직사각형 대원 반구 헤론의공식 ( 세변의길이로삼각형의넓이를구하는공식 ) 육각형 빗변 20 면체 다각형의내심 경사각, 경각, 기울기 원주각 원주 절편호 절편 내부, 안쪽의 교차선 등변사다리꼴 이등변삼각형 카이트 각기둥의옆면적 옆변 옆면 옆표면 직각삼각형에서직각을싸고있는두변 등변사다리꼴의대변 길이 선 선분 T-7686 () 7
linear pair locus of points major arc mean proportional measure of an angle measure of an arc median of a trapezoid median of a triangle midpoint midsegment minor arc n-gon non-collinear non-coplanar non-euclidean geometry obtuse angle obtuse triangle octagon octahedron opposite rays orthocenter orthogonal parabola parallel line segments parallel lines parallelepiped parallelogram pentagon perimeter perpendicular bisector perpendicular bisector concurrence perpendicular lines perpendicular planes 교차선으로만들어진한쌍의각궤적의점장호비례평균각의측량호의측정사다리꼴의중간값삼각형의중앙값중점중간선분단호 n 각형비공선비동일편면상비유쿨리드의기하학둔각둔각삼각형팔각형팔면체반대사선수심직교포물선평행선분평행선평행6면체평행사변형오각형둘레수직이등분선수직이등분선의집합점직각선직각면 T-7686 () 8
pi plane point point of concurrency point of tangency polygon polyhedron prism product property of proportions proportional pyramid Pythagorean Theorem quadrant quadratic equation quadratic formula quadrilateral radius ratio ray real numbers rectangle rectangular solid regular polygon remote interior angles rhombus right angle right triangle scalene triangle secant segment segment of a circle semicircle set 파이면점공점탄젠트의점다각형다면체각기둥비례곱셈법비례각뿔피타고라스의정의사분면이차방정식이차방정식의근의공식사변형반지름비율사선실수직사각형직각정육면체정다각형원격내각마름모꼴직각직삼각형부등변삼각형할선선분, 활꼴원의활꼴, 선분반원집합 T-7686 () 9
similar polygons similar triangles simple quadrilateral skew lines slant height slope sphere square supplementary angles surface area tangent segment tangent to a circle tessellation tetrahedron three-dimensional space topology transformational geometry transversal trapezoid triangle triangle inequality trigonometry of the right triangle two-dimensional space vector vertex vertical angles vertical line volume x-axis x-intercept y-axis y-intercept z-axis 닮은다각형닮은삼각형단일사변형꼬인위치의직선비탈높이기울기구, 구면정사각형보각표면적탄젠트선분원의탄젠트모자이크세공사면체삼차원공간위상수학변형기하학횡단선사다리꼴삼각형삼각부등식정삼각형의삼각법이차원공간벡터꼭지점수직각수직선부피 x-축 x-절편 y-축 y-절편 z-축 T-7686 () 10
Constructions angle bisector bisector center of a regular polygon center of gravity 작도각의이등분선이등분선정다각형의중심중력, 중심 circumcircle (about a polygon) 외접원 ( 다각형의 ) compass construct dynamic geometry software perpendicular bisector perpendicular bisector concurrence perpendicular lines 컴퍼스 ~ 을작도하다, 구성하다다이내믹기하학소프트웨어수직이등분선수직이등분선의집합점직각선 straightedge circle compound locus ellipse hyperbola locus of points parabola Locus 직선자원복합궤적타원쌍곡선궤적의점포물선 궤적 Formal and Informal Proofs AA triangle similarity AAA triangle similarity AAS triangle congruence ASA triangle congruence angle addition postulate axiom biconditional conclusion conditional statement 공식및비공식증명 두각이같으면닮은삼각형임 세각이같으면닮은삼각형임 두각과한변이같은삼각형은합동임 두각과사이에있는한변이같은삼각형은합동임 추가공준각 공리, 원칙 쌍조건문 결론 조건부명제 conjecture 추측 ( 하다 ) conjunction contradiction 논리곱 모순 T-7686 () 11
contrapositive of a statement converse of a statement counterexample deductive reasoning definition disjunction dynamic geometry software equivalence relation Euclidean Parallel Postulate hypotenuse and leg triangle congruence indirect proof inductive reasoning inverse of a statement justify logical equivalent negation parallel postulate(s) postulate proof proof by contradiction Pythagorean Theorem reason reflexive property of equality SAS triangle congruence SAS Similarity Theorem SSS triangle congruence substitution property subtraction property of equality symmetric property of equality theorem transitive property of equality transformational proof truth value two-column proof 대치명제 역명제 반례 연역법 정의 논리합 다이내믹기하학소프트웨어 동치관계 유클리드의평행공준 빗변및나머지두변이같은삼각형의합동 간접증명 귀납적추론 역명제 정당화하다, 해명하다 논리적동치 부정 평행공준 공준 증명 모순을이용한증명 파타고라스의정의 추론하다, 논리적으로생각하다 반사적인상등법칙 두변과한각이같은두삼각형은합동임 한각의크기가같고두변의비율이같은삼각형은닯은삼각형이된다는정리 세변의길이가같으면합동삼각형임 치환법칙 뺄셈의상등법칙 대칭의상등법칙 정리 추이적인상등법칙 변형증명 진리값 이열증명 T-7686 () 12
undefined terms union of sets valid argument Transformational Geometry axis of symmetry center of a dilation center of a rotation 정의를내리기힘든항합집합타당한논쟁변형기하학축의대칭확대의중심회전의중심 clockwise (orientation) 시계방향으로, 오른쪽으로 ( 움직임 ) composition constant of proportionality contraction 합성비례의지속성, 비례상수단축, 축소 counterclockwise (orientation) 시계반대방향으로, 왼쪽으로 ( 움직임 ) dilation direct transformation domain dynamic geometry software fixed point function function notation for transformations glide reflection group half-turn identity image inverse of a transformation isometry mapping (function) 사상 ( 함수 ) opposite transformation orientation preimage 확대직접변환영역다이내믹기하학소프트웨어고정된지점함수, 기능, 작용변환을위한함수표기평행이동과대칭이동이복합적으로된도형의이동집합반회전항등식상역변환등장변환 역변환움직임원상 reflection 대칭 ( 이동 ) rotation 순환, 회전 ( 이동 ) rotational symmetry symmetry T-7686 () 13 순환대칭대칭
tessellation transformation transformational geometry translation Coordinate Geometry abscissa analytical geometry analytical proof Cartesian coordinates Cartesian plane center-radius equation of circle coordinate coordinate geometry coordinate plane distance between two points origin point slope equation of a line rectangular coordinates slope - intercept equation of a line three-dimensional space two-dimensional space vector x-axis x-intercept y-axis y - intercept z-axis 모자이크세공도형의이동변형기하학도형의평행이동좌표기하학가로좌표해석기하학분석적증명데카르트좌표데카르트평면원의중앙반지름방정식좌표좌표기하학좌표평면두점사이의거리원점선의점기울기방정식직교좌표선의기울기-절편방정식삼차원공간이차원공간벡터 x-축 x-절편 y-축 y-절편 z-축 T-7686 () 14