Geometry studies the properties and relationships of points, lines, surfaces, and solids. These vocabulary terms appear frequently in academic writing, standardized tests, and everyday conversation. This guide groups terms by category with definitions, example sentences, and Chinese translations.
Basic 2D Shapes
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Polygon | A closed plane figure with three or more straight sides | A triangle is the simplest polygon with only three sides. | 多边形 |
| Triangle | A three-sided polygon | The roof forms a triangle at the top of the house. | 三角形 |
| Equilateral Triangle | A triangle with all sides equal and all angles 60° | An equilateral triangle has perfect symmetry. | 等边三角形 |
| Isosceles Triangle | A triangle with two equal sides and two equal angles | The bridge support is shaped like an isosceles triangle. | 等腰三角形 |
| Scalene Triangle | A triangle with no equal sides or angles | You cannot fold a scalene triangle evenly in half. | 不等边三角形 |
| Right Triangle | A triangle with one 90° angle | Use a right triangle to calculate the height of the building. | 直角三角形 |
| Quadrilateral | A four-sided polygon | Squares, rectangles, and rhombuses are all quadrilaterals. | 四边形 |
| Square | A rectangle with all sides equal | Fold the paper into a square before cutting it. | 正方形 |
| Rectangle | A quadrilateral with four right angles | Most computer screens are rectangles. | 长方形 |
| Parallelogram | A quadrilateral with opposite sides parallel | A parallelogram can be tilted, unlike a rectangle. | 平行四边形 |
| Rhombus | A parallelogram with all sides equal | A diamond shape in playing cards is a rhombus. | 菱形 |
| Trapezoid | A quadrilateral with one pair of parallel sides | The table has a trapezoid shape, wider at one end. | 梯形 |
| Pentagon | A five-sided polygon | The US Department of Defense building is a pentagon. | 五边形 |
| Hexagon | A six-sided polygon | Beehive cells are hexagons. | 六边形 |
| Heptagon | A seven-sided polygon | A heptagon is less common than a hexagon in nature. | 七边形 |
| Octagon | An eight-sided polygon | Stop signs in most countries are octagons. | 八边形 |
| Nonagon | A nine-sided polygon | Draw a nonagon by connecting nine points on a circle. | 九边形 |
| Decagon | A ten-sided polygon | A decagon has ten vertices and ten edges. | 十边形 |
| Circle | All points at a fixed distance from a center point | The children sat in a circle on the floor. | 圆形 |
| Oval | An elongated circle, like an ellipse | The mirror has an elegant oval shape. | 椭圆形 |
| Sector | A portion of a circle bounded by two radii and an arc | A slice of pizza is a sector of a circle. | 扇形 |
Angles and Lines
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Point | An exact location in space with no size | Mark the point where the two lines cross. | 点 |
| Line | A straight path extending infinitely in both directions | Draw a straight line between the two cities on the map. | 直线 |
| Line Segment | Part of a line with two endpoints | Measure the line segment from A to B. | 线段 |
| Ray | A line with one endpoint extending infinitely in one direction | A ray of sunlight comes through the window. | 射线 |
| Angle | The figure formed by two rays meeting at a common endpoint | Measure the angle between the two walls. | 角 |
| Acute Angle | An angle less than 90° | A 45-degree angle is acute. | 锐角 |
| Right Angle | An angle exactly 90° | The corner of a book forms a right angle. | 直角 |
| Obtuse Angle | An angle greater than 90° but less than 180° | The open door makes an obtuse angle with the wall. | 钝角 |
| Straight Angle | An angle exactly 180°, forming a straight line | A straight angle looks like a flat line. | 平角 |
| Reflex Angle | An angle greater than 180° but less than 360° | A reflex angle is larger than the outside of a corner. | 优角 |
| Complementary Angles | Two angles whose measures sum to 90° | The two acute angles in a right triangle are complementary. | 余角 |
| Supplementary Angles | Two angles whose measures sum to 180° | Adjacent angles on a straight line are supplementary. | 补角 |
| Vertical Angles | Opposite angles formed by intersecting lines | Vertical angles are always equal to each other. | 对顶角 |
| Parallel Lines | Lines that never meet and stay the same distance apart | Railroad tracks are parallel lines. | 平行线 |
| Perpendicular Lines | Lines that intersect at a right angle | The wall and the floor are perpendicular lines. | 垂直线 |
| Transversal | A line that crosses two or more other lines | The transversal creates eight angles with the two parallel lines. | 截线 |
| Bisector | A line that divides an angle or segment into two equal parts | The angle bisector splits the 60° angle into two 30° angles. | 平分线 |
| Collinear | Points that lie on the same straight line | The three dots are collinear along the edge of the ruler. | 共线的 |
| Coplanar | Points or lines that lie in the same plane | All points on a sheet of paper are coplanar. | 共面的 |
Measurement
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Perimeter | The total distance around a polygon | Calculate the perimeter by adding all side lengths. | 周长 |
| Area | The amount of space inside a two-dimensional shape | The area of this room is 20 square meters. | 面积 |
| Volume | The amount of space occupied by a three-dimensional object | The volume of the box is one cubic meter. | 体积 |
| Surface Area | The total area of the outer surface of a 3D object | Paint the surface area of the cube, not just one face. | 表面积 |
| Radius | The distance from the center of a circle to its edge | The radius of the coin is 1 centimeter. | 半径 |
| Diameter | A line through the center of a circle connecting two points on its edge | Double the radius to find the diameter. | 直径 |
| Circumference | The distance around a circle | The circumference of the Earth is about 40,000 kilometers. | 圆周 |
| Chord | A line segment connecting two points on a circle | Find the longest chord, which is the diameter. | 弦 |
| Arc | Part of the circumference of a circle | The arc of the bridge spans 100 meters. | 弧 |
| Degree | A unit for measuring angles (360° in a full circle) | A full rotation measures 360 degrees. | 度 |
| Radian | A unit of angle measure based on the radius of a circle | One radian equals approximately 57.3 degrees. | 弧度 |
| Altitude | The perpendicular height from a base to the opposite vertex | The altitude of the triangle is 5 centimeters. | 高 |
| Base | The bottom side of a geometric figure | Multiply the base by the height to find the area. | 底边 |
| Hypotenuse | The side opposite the right angle in a right triangle | The hypotenuse is the longest side of a right triangle. | 斜边 |
| Diagonal | A line connecting two non-adjacent vertices | Draw a diagonal across the rectangle from corner to corner. | 对角线 |
Transformations
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Translation | Sliding a shape without rotating or flipping it | Translate the triangle 3 units to the right. | 平移 |
| Rotation | Turning a shape around a fixed point | Rotate the square 90 degrees clockwise. | 旋转 |
| Reflection | Flipping a shape over a line to create a mirror image | A reflection in the lake shows the mountain upside down. | 反射 |
| Dilation | Enlarging or reducing a shape proportionally | Dilation changes the size but not the shape. | 缩放 |
| Symmetry | A shape is symmetric if one half mirrors the other | A butterfly has line symmetry down its center. | 对称 |
| Axis of Symmetry | A line dividing a figure into two mirror halves | The letter A has one axis of symmetry. | 对称轴 |
| Rotational Symmetry | A shape looks the same after partial rotation | A snowflake has rotational symmetry of order 6. | 旋转对称 |
| Congruent | Identical in shape and size | The two triangles are congruent because all sides match. | 全等的 |
| Similar | Same shape but different size, with proportional sides | All squares are similar to each other. | 相似的 |
| Scale Factor | The ratio by which a shape is enlarged or reduced | A scale factor of 2 doubles every side length. | 比例因子 |
| Vector | A quantity with both magnitude and direction | Use a vector to describe the translation of the shape. | 向量 |
3D Geometry
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Polyhedron | A solid figure with flat polygonal faces | A cube is a polyhedron with six faces. | 多面体 |
| Face | A flat surface of a polyhedron | Each face of a cube is a square. | 面 |
| Edge | A line segment where two faces meet | Count the edges of a rectangular prism. | 棱 |
| Vertex | A point where edges meet | A cube has eight vertices. | 顶点 |
| Cube | A 3D shape with six equal square faces | Roll the cube to play the board game. | 立方体 |
| Rectangular Prism | A 3D shape with six rectangular faces | A brick is a rectangular prism. | 长方体 |
| Sphere | A perfectly round 3D shape where all surface points are equidistant from the center | A basketball is a sphere. | 球体 |
| Cylinder | A 3D shape with two parallel circular bases and a curved surface | A soup can is a cylinder. | 圆柱体 |
| Cone | A 3D shape with a circular base tapering to a point | An ice cream cone is shaped like a cone. | 圆锥体 |
| Pyramid | A polyhedron with a polygon base and triangular faces meeting at a point | The Great Pyramid of Giza is a square pyramid. | 棱锥体 |
| Triangular Prism | A prism with triangular bases | A Toblerone chocolate box is a triangular prism. | 三棱柱 |
| Torus | A donut-shaped 3D object | A lifebuoy has the shape of a torus. | 环面 |
| Net | A 2D pattern that folds into a 3D shape | Unfold the box and you get its net. | 展开图 |
| Cross Section | The shape you get by cutting through a 3D object | The cross section of a cylinder is a circle. | 横截面 |
| Frustum | The part of a cone or pyramid remaining after cutting off the top | A bucket is shaped like a frustum of a cone. | 平截头体 |
Coordinate Geometry
| Term | Definition | Example Sentence | Chinese |
|---|---|---|---|
| Coordinate Plane | A two-dimensional plane formed by the x-axis and y-axis | Plot the point on the coordinate plane. | 坐标平面 |
| X-Axis | The horizontal axis on a coordinate plane | The x-axis runs left to right. | 横轴 |
| Y-Axis | The vertical axis on a coordinate plane | The y-axis runs bottom to top. | 纵轴 |
| Origin | The point (0,0) where the x-axis and y-axis intersect | Start measuring from the origin. | 原点 |
| Ordered Pair | A pair of numbers (x, y) locating a point on a coordinate plane | The ordered pair (3, 4) represents a point. | 有序数对 |
| Quadrant | One of four sections of a coordinate plane | Point (-2, 3) is in the second quadrant. | 象限 |
| Slope | The steepness of a line, calculated as rise over run | A horizontal line has a slope of zero. | 斜率 |
| Intercept | The point where a line crosses an axis | The y-intercept is where the line crosses the y-axis. | 截距 |
| Midpoint | The point exactly halfway between two points | Find the midpoint by averaging the coordinates. | 中点 |
| Distance Formula | A formula to calculate the length between two points | Use the distance formula to find how far apart the cities are. | 距离公式 |
| Equation of a Line | A linear equation representing all points on a line | Write the equation of a line with slope 2 passing through (0, 1). | 直线方程 |
Using Geometry Terms in Academic Writing
Academic writing demands precise language. Apply these patterns when writing about geometry.
Use precise adjectives instead of vague ones. Say “an equilateral triangle” instead of “a triangle with equal sides.” Say “congruent figures” rather than “figures that are the same.”
Describe relationships using the correct prepositions. A line is perpendicular to another line. A shape is similar to another shape. An angle is bisected by a ray.
Use comparison structures correctly. Write “Figure A is congruent to Figure B” (not “congruent with”). Write “the area of the rectangle is greater than the area of the triangle.”
Place measurement terms correctly. Say “the perimeter of the polygon” (not “the polygon’s perimeter” is equally acceptable, but “the perimeter of” is more formal). Use “with a radius of” as in “a circle with a radius of 5 cm.”
Common academic sentence frames:
- “The shape can be classified as a ___ because ___.”
- “If we rotate the figure by ___ degrees, the resulting image ___.”
- “The transformation preserves ___ but changes ___.”
- “By applying the Pythagorean theorem, we find that ___.”
Practice Exercises
Exercise 1: Matching
Match each term to its definition.
| Term | Definition |
|---|---|
| 1. Hypotenuse | A. A quadrilateral with opposite sides parallel |
| 2. Parallelogram | B. The longest side of a right triangle |
| 3. Circumference | C. The distance around a circle |
| 4. Vertex | D. A point where edges or sides meet |
| 5. Dilation | E. Enlarging or reducing a shape |
Exercise 2: Fill in the Blank
Choose the correct term from the box.
acute, congruent, parallel, radius, translation
- The train tracks run __________ to each other for miles.
- An __________ angle measures less than 90 degrees.
- These two triangles are __________ because all corresponding sides match.
- The __________ of this circle is half its diameter.
- A __________ slides a shape without rotating it.
Exercise 3: True or False
- A square is a type of rectangle. _____
- A scalene triangle has two equal sides. _____
- Volume measures the space inside a 3D shape. _____
- Parallel lines eventually meet at a point. _____
- A reflex angle is greater than 180 degrees. _____
Exercise 4: Sentence Writing
Write one sentence for each term using the word correctly.
- Diameter: _______________________________________________
- Area: _______________________________________________
- Symmetry: _______________________________________________
- Rotation: _______________________________________________
- Polygon: _______________________________________________
Answer Key
Exercise 1: 1-B, 2-A, 3-C, 4-D, 5-E
Exercise 2: 1. parallel, 2. acute, 3. congruent, 4. radius, 5. translation
Exercise 3: 1. True, 2. False (an isosceles triangle has two equal sides), 3. True, 4. False (parallel lines never meet), 5. True
Resources
- Khan Academy Geometry — Free video lessons and practice
- Math Is Fun Geometry — Visual explanations for beginners
- IXL Geometry Practice — Interactive skill-building exercises
- GeoGebra — Free online geometry tool for drawing and exploring
- BBC Bitesize Geometry — UK curriculum-aligned resources
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