LIVE 109: Geometry
토 12:00am–1:15 from 2/24(미국 동부 시간)
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 8:00am in China.
캘린더
강조 표시된 날짜에 수업이 열립니다. 날짜를 클릭해 그날의 주제를 살펴보세요.
컬러 키:
새로운 주제 수업
숙제로 주어진 시험 토론
리뷰
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'm learning a lot 🙂
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!
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.
This comprehensive module helped me a lot with my geometric skills. Highly recommended.
I will really miss this class. Thank you so much
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.
I had a fun time having you as a teacher 💕
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'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
JAANSI PARSA
Vice President of FAMAT • AIME qualifier • President of school's math team • Placed top 5 nationally • Coaches local Mathcounts team • Enjoys reading and spending time with friends
클릭하여 자세히 확인
SRINIVAS ARUN
USA(J)MO Qualifier Since 8th Grade • 2019 National MATHCOUNTS Qualifier for Colorado • 2022 MOP (Math Olympiad Program) Qualifier • 2022 USA(J)MO Bronze Medal • 2021 ARML Perfect Score
클릭하여 자세히 확인