Geometry 아이콘

LIVE 83: Geometry

금ㆍ수 12:00am–1:15 from 6/23(미국 동부 시간)

전체 강좌 정보

이 LIVE 강좌에는 라이브 동영상 강의 25시간과 함께(시간당 21) 이 강좌를 통해 1년간 이용할 수 있는 Loh 교수의 녹화 동영상이 포함되어 있습니다.

We’ve carefully designed our courses to maximize engagement. Each of our LIVE classrooms has at least one staff member for every 13 students. The typical class size is around 30 students.

* The official meeting time for this course is 8:00pm in New York.

진단 시험:

이해할 수 있을까요?새로운 것을 배우게 될까요?

캘린더

강조 표시된 날짜에 수업이 열립니다. 날짜를 클릭해 그날의 주제를 살펴보세요.

컬러 키:

새로운 주제 수업

숙제로 주어진 시험 토론

2023년6월
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2023년7월
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2023년8월
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2023년9월
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리뷰

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

YG

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!

RC

I got a hundred on my 3rd try for the regular but I was not able to get the bonus and a super bonus questions. However after this review a lot of the questions are starting to click even though sometimes it is a little confusing. But eventually I understand what is happening.

WH

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

MT

I will really miss this class. Thank you so much

JY

Very impressive, provides many ways to solve problems. The problems are built like riddles, very clever and they always have clear solutions that are properly explained.

CY

I had a fun time having you as a teacher 💕

EH

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.

JY

I'm learning a lot 🙂

교육과정

20개의 강좌 모임은 수업 16개(아래 1일차부터 16일차로 표시됨) 및 숙제 시험 토론 4개로 나뉩니다. 수업 4강 이후 각 시험 토론 모임이 열립니다.

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

동료 스타

VincentTrang의 프로필 사진
VINCENT TRANG

2022 MOP Qualifier • USAMO silver medalist, 2022 • AIME qualifier since 6th grade • Loves Rubik's cubes

클릭하여 자세히 확인

AndyXu의 프로필 사진
ANDY XU

3-time AIME qualifier • USAJMO qualifier • Member of track team

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Refund Policy

No refund requests will be accepted after the student’s second LIVE session starts; Refund amount: 90% refund in the original payment method or 100% refund in course credits.