#### Geometry

Rapidly teaches geometrical concepts through custom-designed problems that are understandable to students who have not yet taken a proof-based high school geometry course. Covers geometry which appears in MATHCOUNTS, AMC 8, and AMC 10.

저희의 혁신적인 교수법을 아직 확인하지 못하셨다면, visit our home page first하여 온라인 수학 교육의 모습에 대한 **고정관념을 깨보세요**.

#### 클릭하여 음소거

### 이 강좌는 누구에게 적합한가요?

Are you taking any math class from 6th Grade Math through Algebra, and already know the content in our Introduction class? If so, then you are already ready to understand this course. It will efficiently teach you how to think creatively about Geometry, and solve problems beyond the curriculum.

진단 시험:

### 강좌 구조

이 강좌에는 수업 16개와 이 강좌의 4가지 1시간짜리 연습 시험(숙제)을 논의하는 시험 검토 세션 4개까지, 1시간짜리 LIVE 동영상 세션 20개가 포함되어 있습니다. 각각의 수업은 Stars 2명이 함께 가르칩니다. 총 150개 이상의 문제가 있습니다.

여러분에게 익숙하지 않을 여러 문제를 각 수업에서 다루므로, 나만의 해결 방법을 만들어내도록 영감을 줍니다. LIVE 동영상 수업 형식을 통해 아이디어를 제안할 수 있으며, 수업에서 자체적으로 나온 아이디어를 이용해 대안적 해결 방법을 다양하게 구성할 수 있도록 함께 브레인스토밍합니다. 이러한 활동은 수학을 깨칠 수 있게 여러분을 적극적으로 참여시킵니다.

각 연습 시험에는 20문제가 있고, 절반은 평균 난이도이며 절반은 아주 어렵습니다.

### 리뷰

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

### 교육과정

**1일차**

Exterior and interior angles; degrees in a circle; symmetry; sum of angles in triangle; altitude and area of an equilateral triangle; Pythagorean Thm; simplifying radicals; similar triangles and area scaling; 30°-60°-90° triangles; trick for squaring numbers ending in 5

**2일차**

Regular octagons; right isosceles triangles; similar triangles; Pythagorean Thm; simplifying radical denominators; variable equations; polygon area; midpoints; corresponding and alternate interior angles; angle-chasing method

**3일차**

Areas of circular sections; areas of intersections of circles; radius; equilateral triangles; inscribed angles and arcs; area of a triangle; 30°-60°-90° right triangles; area of a lune; ratios of areas of similar figures

**4일차**

Area of parallelograms; altitude of a triangle; special triangles (3-5-7, right, obtuse); exterior angles; manipulating diagrams; 30°-60°-90° triangles; isosceles trapezoids; factoring; variable equations

**5일차**

Right trapezoids; 8-15-17 right triangles; Pythagorean Thm; AAA similarity and scaling; corresponding angles; simplifying ratios; kite area and diagonals; angle chasing; symmetry; complementary angles

**6일차**

Inscribed and central angles; inscribed angle thm; isosceles triangles; supplementary angles; exterior angle thm; variables; arc measure; subtended arcs; secant lines; intersecting secant angle thm; angles of intersecting chords

**7일차**

Chords; midpoints; 8-15-17 and 3-4-5 right triangles; ratios and scaling; inscribed angles and arcs; congruency; Pythagorean Thm; similar triangles; intersecting chords thm; difference of squares; common chords; circumscribed circle on three points

**8일차**

Cyclic quadrilaterals; arc measure; inscribed angles; degrees in a circle; exterior angle thm; supplementary angles; intersecting chord angle thm; counting; secant and tangent lines to a circle; secant-tangent product thm

**9일차**

Concentric circles; right triangles; Pythagorean Thm; symmetry; angle between radius and tangent of a circle; congruent triangles; simplifying radicals; externally tangent circles; equilateral triangles; areas of circular sectors

**10일차**

Angle between tangent and chord to a circle; angle between radius and tangent; intersecting chord angle thm; secant-tangent and tangent-tangent inscribed angles; angles of cyclic quadrilaterals; inscribed angle thm; proof techniques

**11일차**

External and internal tangents to two circles; parallel lines and corresponding angles; Pythagorean Thm; 5-12-13 and 3-4-5 right triangles; similar triangles and scaling; prime numbers; manipulations of diagrams

**12일차**

Tangent-tangent segments to a circle; Pythagorean Thm; kites; similar triangles; angle bisector; area and sums of pairs of sides of quadrilateral with inscribed circle; area of a triangle

**13일차**

Angle bisector thm; isosceles and congruent triangles; area and altitude of a triangle; ratios and scaling; golden ratio; simplifying radical denominators; proof of angle bisector thm; inscribed circle in a triangle; estimation

**14일차**

Reflected angles; minimizing path length; triangle inequality; opposite interior angles; congruency; transversals and corresponding angles; Pythagorean Thm; 3-D path length; manipulating 3-D diagrams; estimation

**15일차**

Triangle inequality; counting; case analysis

**16일차**

Special triangles; area of a triangle; Pythagorean triples; scaling; proof of Heron's formula; semiperimeter; Pythagorean Thm; polynomials; common chord to two circles; 30°-60°-90° triangle

### 등록

We will offer the LIVE version of this course in Summer 2023.

일정에 맞출 수 없거나 이미 특별히 동기가 강한 학생들을 위해, 자기 진도 맞춤형 버전에는 이 주제에 대한 Loh 교수의 가르침이 모두 포함되어 있습니다. 원하는 형식을 선택해 등록하세요.