📚 IGCSE Maths G-1 Workbook 200: Core Geometry Revision | IGCSE数学G-1练习册200：几何核心复习
This article is designed for IGCSE students working through the G-1 Workbook 200, a focused collection of 200 exercises that target essential geometry topics. We will walk through the core concepts, common question patterns, and efficient problem-solving strategies to help you master this revision series.
本文专为正在使用 G-1 练习册 200 的 IGCSE 学生编写。该练习册包含 200 道针对性习题，聚焦几何核心知识点。我们将系统梳理核心概念、常见题型与高效解题策略，帮助你熟练掌握这套复习资料。
1. Angle Basics | 角度基础
Angles on a straight line sum to 180°.
直线上的角之和等于 180°。
Vertically opposite angles are equal.
对顶角相等。
When a transversal crosses two parallel lines, corresponding angles are equal, alternate interior angles are equal, and interior angles on the same side are supplementary (sum to 180°).
当一条截线与两条平行线相交时，同位角相等，内错角相等，同旁内角互补（和为 180°）。
In the G-1 Workbook 200, you frequently need to combine these angle rules to find missing angle measures in diagrams.
在 G-1 练习册 200 中，经常需要综合运用这些角度规则来求解图形中的未知角度。
2. Triangle Properties | 三角形性质
The sum of interior angles in any triangle is 180°.
任意三角形的内角和为 180°。
The exterior angle of a triangle equals the sum of the two opposite interior angles.
三角形的外角等于与它不相邻的两个内角之和。
An isosceles triangle has two equal sides and two equal base angles.
等腰三角形的两条腰相等，两个底角相等。
An equilateral triangle has three equal sides and each angle is 60°.
等边三角形的三条边都相等，每个角都是 60°。
Remember the triangle inequality: the sum of any two sides must be greater than the third side.
牢记三角形不等式：任意两边之和必须大于第三边。
3. Polygons and Angle Sum | 多边形与内角和
For an n-sided polygon, the sum of interior angles is given by:
对于 n 边形，其内角和为：
(n – 2) × 180°
For a regular polygon, each interior angle equals (n – 2) × 180° / n.
正多边形的每个内角等于 (n – 2) × 180° / n。
The sum of exterior angles of any polygon is always 360°.
任意多边形的外角和恒为 360°。
The number of diagonals in an n-sided polygon is n(n – 3) / 2.
n 边形的对角线数为 n(n – 3) / 2。
Workbook 200 questions often ask you to find the number of sides from a given interior angle, or vice versa.
练习册 200 中的题目常要求你根据给定的内角求边数，或根据边数求内角。
4. Congruent Triangles | 全等三角形
Two triangles are congruent if their corresponding sides and angles are equal.
若两个三角形的对应边和对应角都相等，则它们全等。
The congruence criteria are SSS, SAS, ASA, AAS, and RHS (only for right-angled triangles).
全等判定条件有 SSS、SAS、ASA、AAS 以及 RHS（仅适用于直角三角形）。
Be careful: SSA does not guarantee congruence.
注意：SSA 不能判定三角形全等。
When using congruence, always state the condition and the corresponding vertices in the correct order.
运用全等时，务必写明判定条件，并按正确顺序写出对应顶点。
5. Similar Triangles | 相似三角形
Two triangles are similar if their corresponding angles are equal (AA condition).
若两个三角形的对应角相等，则它们相似（AA 条件）。
Similar triangles have corresponding sides in the same ratio.
相似三角形的对应边成比例。
The ratio of perimeters of similar triangles equals the scale factor.
相似三角形的周长比等于相似比。
The ratio of areas of similar triangles equals the square of the scale factor.
相似三角形的面积比等于相似比的平方。
In the workbook, look for parallel lines or shared angles to establish similarity quickly.
在练习册中，可以通过平行线或公共角快速判定相似。
6. Pythagoras’ Theorem | 勾股定理
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:
在直角三角形中，斜边的平方等于两直角边的平方和：
a² + b² = c²
The converse is also true: if a² + b² = c², then the triangle is right-angled.
逆定理也成立：若一个三角形的三边满足 a² + b² = c²，那么这个三角形是直角三角形。
Common Pythagorean triples include 3-4-5, 5-12-13, and 8-15-17.
常见的勾股数有 3-4-5、5-12-13 和 8-15-17。
Always identify the hypotenuse (the side opposite the right angle) before applying the theorem.
应用定理前，务必先确认斜边（直角所对的边）。
7. Basic Circle Properties | 圆的基本性质
A circle has radius, diameter, chord, arc, sector, and segment.
圆包含半径、直径、弦、弧、扇形和弓形等元素。
The angle subtended by a diameter at the circumference is always 90°.
直径所对的圆周角总是 90°。
Angles subtended by the same arc at the circumference are equal.
同一弧所对的圆周角相等。
The angle at the centre is twice the angle at the circumference when both subtend the same arc.
当圆心角和圆周角对应同一弧时，圆心角是圆周角的两倍。
These properties are tested extensively in the G-1 Workbook 200, especially in multi-step circle geometry problems.
这些性质在 G-1 练习册 200 中被广泛考查，尤其是在多步圆几何题中。
8. Tangents to a Circle | 圆的切线
A tangent to a circle is perpendicular to the radius at the point of contact.
圆的切线在切点处与过该点的半径垂直。
From an external point, the two tangent lengths to a circle are equal.
从圆外一点引圆的两条切线，其切线长相等。
The tangent-chord theorem states that the angle between a tangent and a chord equals the angle in the alternate segment.
弦切角定理指出：切线与弦的夹角等于该弦所对的圆周角（在另一个弓形内的角）。
When solving tangent problems, draw the radius to the tangent point and look for right angles.
解答切线问题时，画出切点与圆心的半径，并寻找直角。
9. Perimeter and Area | 周长与面积
Regular shapes you must know:
你必须掌握的基本图形：
-
Rectangle: Area = length × width, Perimeter = 2(length + width)
矩形：面积 = 长 × 宽，周长 = 2(长 + 宽)
-
Triangle: Area = ½ × base × height
三角形：面积 = ½ × 底 × 高
-
Parallelogram: Area = base × height
平行四边形：面积 = 底 × 高
-
Trapezium: Area = ½ × (a + b) × height
梯形：面积 = ½ × (上底 + 下底) × 高
-
Circle: Area = πr², Circumference = 2πr
圆：面积 = πr²，周长 = 2πr
For sectors, the arc length and area are fractions of the full circle based on the central angle θ:
扇形的弧长和面积是圆的一部分，其比例由圆心角 θ 决定：
Arc length = (θ/360°) × 2πr, Sector area = (θ/360°) × πr²
10. Volume and Surface Area | 体积与表面积
Prisms have a uniform cross-section. Volume = area of cross-section × length.
棱柱具有均匀截面。体积 = 截面积 × 长度。
Cylinder: Volume = πr²h, Curved surface area = 2πrh, Total surface area = 2πrh + 2πr².
圆柱：体积 = πr²h，侧面积 = 2πrh，表面积 = 2πrh + 2πr²。
Sphere: Volume = 4/3 πr³, Surface area = 4πr².
球：体积 = 4/3 πr³，表面积 = 4πr²。
Cone: Volume = 1/3 πr²h, Curved surface area = πrl (where l is the slant height).
圆锥：体积 = 1/3 πr²h，侧面积 = πrl（其中 l 为母线长）。
In the Workbook 200, check whether the question asks for total surface area or curved surface area to avoid losing marks.
在练习册 200 中，要仔细审题，看清是求总表面积还是侧面积，避免失分。
11. Coordinate Geometry Basics | 坐标几何基础
The distance between two points (x₁, y₁) and (x₂, y₃) is given by:
两点 (x₁, y₁) 和 (x₂, y₂) 之间的距离公式为：
√[(x₂ – x₁)² + (y₂ – y₁)²]
The midpoint of the segment joining two points is:
连接两点的线段中点为：
((x₁ + x₂)/2, (y₁ + y₂)/2)
The gradient (slope) of a line through two points is:
通过两点的直线梯度（斜率）为：
(y₂ – y₁) / (x₂ – x₁)
Parallel lines have equal gradients; perpendicular lines have gradients that multiply to -1 (m₁ × m₂ = -1).
平行线的斜率相等；互相垂直的直线斜率之积为 -1（m₁ × m₂ = -1）。
Mastering these twelve areas will give you a solid foundation for the G-1 Workbook 200 and for the IGCSE geometry paper. Practice each type until you can apply the rules quickly and accurately. Always draw a clear diagram and label known values before starting your solution.
掌握以上十二个专题将为你学习 G-1 练习册 200 和 IGCSE 几何试卷打下坚实基础。请针对每种题型反复练习，直到能快速、准确地运用相关规则。解题前务必画清图形，并标出已知数值。
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