#### 几何工具

通过精心编写的题目，快速深化几何概念的理解，即使学生尚未学习高中几何证明课程，也可以轻松学习。该课程难度范围覆盖MATHCOUNTS、AMC 8 和 AMC 10。

想了解我们独具一格的教学方法？visit our home page first，来看看我们是如何打破线上数学课的固定框架的吧！

#### 点击开启麦克风

### 这门课适合我吗？

你是否正在上从6年级数学到代数的数学课程，并且已经了解综合入门课程中的内容？如果是的话，你已经具备了足够的能力来加入这门课。这门课将带你高效学习如何更具创造力地思考几何，轻松应对比学校课程更难的题目。

不知道课程是否合适？来挑战一下能力水平测试吧！

### 课程结构

每个模块的课程均包含20节LIVE课程，分为16节【日挑战】课程和4节【单元考核测验】复习课程（学生需要在复习课前进入配套的Pre-Recorded课程完成测验）。每节课程都将由2位 Stars 共同授课。在该模块的学习中，我们将讨论超过150个数学问题。

【日挑战课程】每节课中，学生都会学习解决全新的数学问题，老师们将通过启发式的教学引导和鼓励学生开创自己的解题方法。我们的LIVE课堂赞赏学生们提出自己的想法，鼓励每个学生和全班同学一起集思广益，构建各种不同的解题方法，更积极地参与数学发现。

【单元考核测验】包含20道数学问题，其中10题在正常难度范围内，而另外10题则非常具有挑战性。

### 学生评价

This is really helpful. I used to suck at geometry and had little to no interest in it. After I used this course, I had drastic improvements in Geometry. definitely would recommend

Before I took this course, geometry was a part of math that I was okay at, but didn't consider one of my top aspects of mathematics. As I took this course, I began to discover the other side of geometry, and how it was in fact a very important part of math. Now, I consider geometry as one of my favorite parts of math to work with, thanks to this course!

Geometry Tools is a great course if you want to learn more about Geometry. Professor Po Shen Loh teaches a lot of great tricks that you can use to solve some difficult problems. I have learned a lot of tricks and tips, including how to square a number, that ends in 5, in just a few seconds. After I completed only 15% of the course, I learned a lot of material that I had not learned in school. I improved greatly on most of my geometry tests. I am very happy about my improvement in Geometry and plan to take the Module 3: Combinatorics Tools and Module 4: Algebra Tools. Thank you, Professor Po Shen Loh, for taking your time to make videos to try to help younger people, and I hope you make more courses!

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

This is a very fun (but hard!) course. I like how the problems are given to introduce new concepts and the solutions are very clear, and how even though there's a lot of stuff covered, it's presented in only a few problems.

I really like the seminar, it is interesting and challenging; and hard of course. Dr. Po did a great job explaining the question using different approaches.

muy bien

This is really helpful. I used to suck at geometry and had little to no interest in it. After I used this course, I had drastic improvements in Geometry. definitely would recommend

Before I took this course, geometry was a part of math that I was okay at, but didn't consider one of my top aspects of mathematics. As I took this course, I began to discover the other side of geometry, and how it was in fact a very important part of math. Now, I consider geometry as one of my favorite parts of math to work with, thanks to this course!

Geometry Tools is a great course if you want to learn more about Geometry. Professor Po Shen Loh teaches a lot of great tricks that you can use to solve some difficult problems. I have learned a lot of tricks and tips, including how to square a number, that ends in 5, in just a few seconds. After I completed only 15% of the course, I learned a lot of material that I had not learned in school. I improved greatly on most of my geometry tests. I am very happy about my improvement in Geometry and plan to take the Module 3: Combinatorics Tools and Module 4: Algebra Tools. Thank you, Professor Po Shen Loh, for taking your time to make videos to try to help younger people, and I hope you make more courses!

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

This is a very fun (but hard!) course. I like how the problems are given to introduce new concepts and the solutions are very clear, and how even though there's a lot of stuff covered, it's presented in only a few problems.

I really like the seminar, it is interesting and challenging; and hard of course. Dr. Po did a great job explaining the question using different approaches.

muy bien

This is really helpful. I used to suck at geometry and had little to no interest in it. After I used this course, I had drastic improvements in Geometry. definitely would recommend

Before I took this course, geometry was a part of math that I was okay at, but didn't consider one of my top aspects of mathematics. As I took this course, I began to discover the other side of geometry, and how it was in fact a very important part of math. Now, I consider geometry as one of my favorite parts of math to work with, thanks to this course!

Geometry Tools is a great course if you want to learn more about Geometry. Professor Po Shen Loh teaches a lot of great tricks that you can use to solve some difficult problems. I have learned a lot of tricks and tips, including how to square a number, that ends in 5, in just a few seconds. After I completed only 15% of the course, I learned a lot of material that I had not learned in school. I improved greatly on most of my geometry tests. I am very happy about my improvement in Geometry and plan to take the Module 3: Combinatorics Tools and Module 4: Algebra Tools. Thank you, Professor Po Shen Loh, for taking your time to make videos to try to help younger people, and I hope you make more courses!

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

This is a very fun (but hard!) course. I like how the problems are given to introduce new concepts and the solutions are very clear, and how even though there's a lot of stuff covered, it's presented in only a few problems.

I really like the seminar, it is interesting and challenging; and hard of course. Dr. Po did a great job explaining the question using different approaches.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

This comprehensive module helped me a lot with my geometric skills. Highly recommended.

muy bien

### 课程大纲

**第1课**

内⻆和外⻆、圆的度数、对称、三⻆形内⻆和、等边三⻆形的高和面积、勾股定理、根式的简化、相似三⻆形及其面积比例、30°-60°-90°三⻆形、以5结尾的数字平方技巧

**第2课**

正八边形、等腰直⻆三⻆形、相似三⻆形、勾股定理、根式分母的简化、方程组、多边形面积、中点、平行线同位⻆及内错⻆性质、追⻆法

**第3课**

圆形截面面积、圆的重叠部分面积、半径、等边三⻆形、圆周⻆的⻆度及其对应弧⻓、三⻆形面积、30°-60°-90°直⻆三⻆形、月牙型面积、相似图形的面积比

**第4课**

平行四边形面积、三⻆形的高、特殊三⻆形(3-5-7边⻓三⻆形、直⻆三⻆形、钝⻆三⻆形)、外⻆、图形变换、30°-60°-90°三⻆形、等腰梯形、因式分解、方程组

**第5课**

直⻆梯形、 8-15-17边⻓直⻆三⻆形、勾股定理、⻆-⻆-⻆相似三⻆形及比例、同位⻆、简化比例、筝形面积和对⻆线性质、追⻆法、对称、余⻆

**第6课**

圆周⻆和圆心⻆、圆周⻆定理、等腰三⻆形、补⻆、外⻆定理、变量、弧度、任意⻆所对应的圆弧、割线、切割线定理、相交弦所成⻆度

**第7课**

弦、中点、8-15-17边⻓直⻆三⻆形、3-4-5边⻓直⻆三⻆形、边⻓和面积比、圆周⻆和弧度、全等图形、勾股定理、相似三⻆形、相交弦定理、平方差、两圆公共弦、三⻆形外接圆

**第8课**

圆内接四边形、弧度、圆周⻆、圆的度数、外⻆定理、补⻆、相交弦所成⻆度定理、计数、圆的割线和切线、割切线定理

**第9课**

同心圆、直⻆三⻆形、勾股定理、对称、圆的切线及过其切点的半径所成⻆度、全等三⻆形、根式的简化、外切圆、等边三⻆形、扇形面积

**第10课**

切线和弦的夹⻆、圆的切线及过其切点的半径所成⻆度、相交弦⻆定理、切割线内⻆、切线-切线内⻆、圆内接四边形⻆度、圆周⻆定理、证明技巧

**第11课**

两圆内外切线、平行线和同位⻆、勾股定理、5-12-13边⻓和3-4-5边⻓直⻆三⻆形、相似三⻆形及其比例、质数、图形变换

**第12课**

过圆外一点的切线线段、勾股定理、筝形、相似三⻆形、⻆平分线、带内切圆的四边形的面积和数量、三⻆形面积

**第13课**

⻆平分线定理、等腰全等三⻆形、三⻆形的面积和高、比、⻩金比例、根式分母的简化、⻆平分线定理的证明、三⻆形的内接圆、估算

**第14课**

反射⻆、最短路径、三⻆形不等式、内对⻆、全等、截线和同位⻆、勾股定理、3-D路径⻓度、3-D图形处理、估算

**第15课**

三⻆形不等式、计数、案例分析

**第16课**

特殊三⻆形、三⻆形的面积、毕氏三数、比例、海伦公式证明、半周⻓、勾股定理、多项式、两圆 公共弦、30°-60°-90°⻆度三⻆形

### 报名课程

每位报名LIVE在线直播课的学生都将同时享有对应的Pre-Recorded自学录播课程一年使用权，无需额外购买。LIVE直播课经过罗教授和教学团队精心设计的，通过前所未有的引人入胜的教学方式、极为丰富的课堂交互体验，让学生在趣味学习中爱上挑战和思考。 以下所有直播课显示时间均为您的当地时间（美国将于2023年3月12日星期日进入夏令时，请其他国家和地区的学生注意课程时间调整）。

如果你有强大的自驱力可以进行自主学习，或者想比LIVE课程安排更快地完成一个模块的学习，也欢迎你选择我们的自学录播课程。录播课包含了所有罗教授关于该模块的教学视频（没有直播课堂），在过去3年中也有数千名来自世界各地的同学参与学习。