#### LIVE 109: Geometry

Sa 12:00–1:15am from 2/24 (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 8:00am in China.

Diagnostic Tests:

### Calendar

Classes will meet on the highlighted dates. Click on any date to view the topics for that day.

Color Key:

Lesson on new topic

Discuss homework challenge

### 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 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

I'm learning a lot 🙂

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

I will really miss this class. Thank you so much

I had a fun time having you as a teacher 💕

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

**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

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**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

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