THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary,

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High School Level Glossary Geometry Glossary /

accommodations for ELL/LEP students Last Updated:

1 High School Level Glossary Geometry Glossary / Traditional 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

2 THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary, and Continuing Education and Office of Higher Education Office of Bilingual Education and Foreign Language Studies 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 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

3 Problem Solving AA triangle similarity AAA triangle similarity AAS triangle congruence additive property of equality algorithm apply ASA triangle congruence conjecture constraints construct discover dynamic geometry software explore generalization inductive reasoning justify parameters reason truth value valid argument Reasoning and Proof AA triangle similarity AAA triangle similarity AAS triangle congruence analytical proof angle addition postulate ASA triangle congruence axiom biconditional conclusion 解題兩個角相等 (AA) 的三角形的相似性三個角相等 (AAA) 的三角形的相似性角角邊 (AAS) 三角形的全等性相等式加法性質規則系統算法應用運用把... 施 ( 用 ) 於角邊角 (ASA) 三角形的全等性推測約束限制作圖構造發現動態幾何軟件探索概括化普遍化歸納推理證明參數理由真值有效的論證推論與證明兩個角相等 (AA) 的三角形的相似性三個角相等 (AAA) 的三角形的相似性角角邊 (AAS) 三角形的全等性解析證明角相加的公理角邊角 (ASA) 三角形的全等性公理雙向條件結論 T-7686 () 1

4 conditional statement 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 hypotenuse and leg triangle congruence 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 條件陳述推測連接矛盾逆否語句經過質位變換產生的語句逆語句反例反證演繹證明演繹推理定義分離分裂動態幾何軟件等值關係歐幾里得平行公理解釋幾何斜邊與三角形的直角邊的全等性假設間接證明歸納推理逆語句調查證明邏輯等值相反否定段落證明法平行公理證明反證法成比例的勾股定理畢氏定理理由等式自反性 T-7686 () 2

5 SAS triangle congruence 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 axiom biconditional compound statement conclusion conditional statement conjecture conjunction contrapositive of a statement converse of a statement definition disjunction explain hypothesis inverse of a statement justify negation theorem 邊角邊 (SAS) 三角形的全等性邊角邊 (SAS) 三角形的相似性定理邊邊邊 (SSS) 三角形的全等性代入性質等式減法性質等式對稱性質定理變換證明等式可遞性質真值兩行式證明未定義詞項並集合集有效的論證通信聯絡傳送公理雙向條件復合陳述結論條件陳述推測連接逆否語句經過質位變換產生的語句逆語句定義分離分裂解釋假設逆語句證明相反否定定理 T-7686 () 3

6 truth value undefined terms Connections 真值未定義詞項連接 apply compound locus discover intersection of sets investigate spatial relationships union of sets 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 應用運用把... 施 ( 用 ) 於複合軌跡發現集的交點調查空間關係並集合集表述解析幾何坐標幾何定義歐幾里得幾何函數圖形表述點的軌跡邏輯等值非歐幾里得幾何三維空間圖形變換幾何二維空間幾何關係兩個角相等 (AA) 的三角形的相似性三個角相等 (AAA) 的三角形的相似性角角邊 (AAS) 三角形的全等性角邊角 (ASA) 三角形的全等性絕對值銳角銳角三角形 T-7686 () 4

7 adjacent angles 鄰角 algebraic representation 代數表述 alternate interior angles 内錯角 altitude 高線頂垂線 analytical geometry 解析幾何 angle 角 angle bisector 角的等分線 angle measure 角的度量 apothem 邊心距 arc 弧 arc measure 弧的度量 area 面積 axis of symmetry 對稱軸 base 底 ( 邊 ) 底數基數 betweeness 中間性介於 bisector 等分線 center of a circle 圓心 center of a regular polygon 正多邊形的中心點 center of gravity 重心 central angle 圓心角 central angle of a regular polygon 正多邊形的圓心角 centroid 形心重心矩心 chord 弦 circle 圓 circumcenter 外心外接圓心 circumcircle (about a polygon) 外接圓 ( 多邊形 ) circumference 圓周 collinear points 共線點 common tangents 公切線 complementary angles 餘角 concave polygon 凹多邊形 concentric circles 同心圓 concurrent lines 共點線 T-7686 () 5

8 cone 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 圓錐體全等圓錐截面比例常數凸多邊形坐標幾何共面的對應角對應部分對應邊交叉部分立方體圓柱體定義對角線直徑二面角距離點與線之間的距離兩條平行線之間的距離兩個點之間的距離 12 面體橢圓形端點等角的等距的等邊三角形等邊多邊形歐幾里得幾何歐幾里得平行公理外部的外角外部割線 T-7686 () 6

9 face of a polyhedron 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 多面體的面高線的底部函數幾何平均值幾何黃金比例黃金長方形大圓半圓海倫公式六邊形 ( 直角三角形中的 ) 斜邊二十面體多邊形内心傾角斜角圓周角内切圓截弧截距内部的相交直線等腰梯形等腰三角形風箏棱柱體的側面積側棱側面側表面直角三角形的直角邊等腰梯形的邊長線線段 T-7686 () 7

10 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 一對互為補角的角點的軌跡優弧大于半圓的弧比例中項角的度數弧的度量梯形的中線三角形的中線中點中間段小弧劣弧 n 邊形不共線的不共面的非歐幾里得幾何鈍角鈍角三角形八邊形八面體反向射線垂心正交的抛物線平行線段平行線平行六面體平行四邊形五邊形周長垂直平分線垂直平分線交點垂直線垂直面 T-7686 () 8

11 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 圓周率面點交點切點多邊形多面體棱柱體比例的乘積性質比例的棱錐棱錐體勾股定理畢氏定理象限二次方程二次公式四邊形半徑比率射線實數長方形長方形立體正多邊形不相鄰内角菱形直角直角三角形不等邊三角形割線線段弓形半圓集 T-7686 () 9

12 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 相似多邊形相似三角形簡單四邊形斜直線斜高斜率坡度球體球面平方互補角表面積切線段圓的切線花紋鑲嵌四面體三維空間拓撲學圖形變換幾何橫截的橫向的梯形三角形三角不等式直角三角形三角學二維空間矢量項點對頂角垂直線體積容積 x- 軸 x- 截距 y- 軸 y- 截距 z- 軸 T-7686 () 10

13 Constructions 作圖構造 angle bisector 角的等分線 bisector 等分線 center of a regular polygon 正多邊形的中心點 center of gravity 重心 circumcircle (about a polygon) 外接圓 ( 多邊形 ) compass 圓規 construct 作圖構造 dynamic geometry software 動態幾何軟件 perpendicular bisector 垂直平分線 perpendicular bisector concurrence 垂直平分線交點 perpendicular lines 垂直線 straightedge 邊直尺 Locus 軌跡 circle compound locus ellipse hyperbola locus of points parabola 圓複合軌跡橢圓雙曲線點的軌跡抛物線 Formal and Informal Proofs AA triangle similarity AAA triangle similarity AAS triangle congruence ASA triangle congruence angle addition postulate axiom biconditional conclusion conditional statement conjecture 正規與非正規證明兩個角相等 (AA) 的三角形的相似性三個角相等 (AAA) 的三角形的相似性角角邊 (AAS) 三角形的全等性角邊角 (ASA) 三角形的全等性角相加的公理公理雙向條件結論條件陳述推測 T-7686 () 11

14 conjunction contradiction 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 連接矛盾逆否語句經過質位變換產生的語句逆語句反例反證演繹推理定義分離分裂動態幾何軟件等值關係歐幾里得平行公理斜邊與三角形的直角邊的全等性間接證明歸納推理逆語句證明邏輯等值相反否定平行公理公理證明反證法勾股定理畢氏定理理由等式自反性邊角邊三角形 (SAS) 的全等性邊角邊三角形 (SAS) 的相似性定理邊邊邊三角形 (SSS) 的全等性代入性質等式減法性質等式對稱性質定理等式可遞性質變換證明 T-7686 () 12

15 truth value two-column proof undefined terms union of sets valid argument Transformational Geometry 真值兩行式證明未定義詞項並集合集有效的論證變換幾何 axis of symmetry 對稱軸 center of a dilation 膨脹中心 center of a rotation 旋轉中心 clockwise (orientation) 順時針 ( 方向 ) composition 復合合成 constant of proportionality 比例常數 contraction 縮小 counterclockwise (orientation) 逆時針 ( 方向 ) dilation 膨脹 direct transformation 直接變換 domain 域定義域 dynamic geometry software 動態幾何軟件 fixed point 不懂點固定點 function 函數 function notation for transformations 函數變換符號 glide reflection 滑動反射 group 群 half-turn 轉 180 度 identity 恒等式 image 映像 inverse of a transformation 逆變換 isometry 等距 mapping (function) 映射 ( 函數 ) opposite transformation 逆變換 orientation 定方向 preimage 逆象原象 reflection 反射 T-7686 () 13

16 rotation rotational symmetry symmetry tessellation transformation transformational geometry translation Coordinate Geometry 旋轉旋轉對稱對稱花紋鑲嵌變換變換幾何轉化坐標幾何 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 橫坐標解析幾何解析證明直角坐標笛卡爾坐標笛卡爾平面圓的中心 - 半徑公式坐標坐標幾何坐標平面兩個點之間的距離原點線的點斜式方程式長方形坐標線的斜截式方程式三維空間二維空間矢量 x- 轴 x- 截距 y- 轴 y- 截距 z- 軸 T-7686 () 14

THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary,

THE STATE EDUCATION DEPARTMENT / THE UNIVERSITY OF THE STATE OF NEW YORK / ALBANY, NY Education - P-16 Office of Elementary, Middle, Secondary, High School Level Glossary Geometry Glossary / Chinese Simplified Translation of Geometry terms based on the Coursework for Geometry Grades 9 to 12. Word-for-word glossaries are used for testing accommodations