LIVE 148: Geometry
Sa 1:00–2:15am from 10/26 (Your Time*)
This LIVE course contains a total of 25 hours of live video instruction (~$21/hour), plus 1 year of access to Prof. Loh's recorded videos from this course.
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 9:00am in China.
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Classes will meet on the highlighted dates. Click on any date to view the topics for that day.
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Reviews
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 🙂
Syllabus
The 20 course meetings are split in 16 lessons (called Day 1 through Day 16 below), and 4 homework exam discussions. Each exam discussion meeting happens after 4 lessons.
Day 1
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
Day 2
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
Day 3
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
Day 4
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
Day 5
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
Day 6
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
Day 7
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
Day 8
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
Day 9
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
Day 10
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
Day 11
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
Day 12
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
Day 13
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
Day 14
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
Day 15
Triangle inequality; counting; case analysis
Day 16
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
Co-Stars
SRIRAM KALKI
National MATHCOUNTS competitor for Kansas • 2-time AIME qualifier • USACO silver
click for more
YIKAI ZHAO
USAMO qualifier • USACO Platinum • Chinese National Olympiad in Informatics in Provinces (NOIP) First Prize Member of Student Council • Enjoys chess, reading, and tennis
click for more