#### Geometry

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

If you haven't yet seen our revolutionary teaching method, visit our home page first, to **shatter your expectations** of what online math looks like.

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### Who Is This Course For?

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

Diagnostic Tests:

### Course Structure

This course contains 20 LIVE 1-hour video sessions, of which 16 are lessons, and 4 are exam review sessions that discuss the course's 4 practice 1-hour exams (homework). Each class is co-taught by 2 of our Stars. In total, there are over 150 problems.

Each lesson contains several problems which are meant to be unfamiliar to you, so that they inspire you to invent your own solutions. In our LIVE video class format, you propose your ideas, and we brainstorm together with you to construct a variety of alternative solutions using the class's own ideas. This actively involves you in discovering mathematics.

Each practice exam contains 20 problems, of which half are of average difficulty, and the other half are very challenging.

### 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

**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

### Enroll

We have LIVE and self-paced versions of this course. We strongly recommend the LIVE format, as it has been carefully designed to be so engaging that students fall in love with challenge. There has never been anything like it before. All times are listed in your local time zone.

For students who want to learn a subject sooner than a LIVE course matches their schedule, our self-paced version contains all of Prof. Loh's teaching on the subject (without live teaching). This is available on our self-paced course platform, where thousands of students have learned over the past 3 years.