# High School Geometry and Introductory Linear Algebra

Next session on Dec 5, 2022

Hosted by Jose Roberto Cossich G

### Series Details

About

Hey guys,

I decided to make a new, comprehensive series on Geometry, including matrices, vectors, and other concepts to discuss planes, shapes in 3-dimensions, etc.

IMPORTANT: You can join this series AFTER it has begun in case there are any specific topics you would like to learn or review!

This series we will covering all Khan Academy Courses on Basic Geometry, High School Geometry, as well as an introduction to linear algebra.

The units we'll be doing are the following:

Geometry Foundations, Triangles, Area and Perimeter, Surface Area and Volume, Polygons, Performing Transformations, Transformation properties and proofs, Congruence, Similarity, Analytical Geometry, Conic Sections, Circles, and Solid Geometry, Vectors and Matrices, and Planes.

This series is for students who have already completed Pre-algebra and Arithmetic and are eager to learn! Some units may require some knowledge of Algebra 1, but we will cover that as well in our sessions.

✋ ATTENDANCE POLICY

I try to make the session times as accommodating as possible, however make-up sessions are always available.

Dates

November 13 - May 21

Learners

59 / 75

Total Sessions

25

### About the Tutor

Hi, my name's Jose, I'm a Junior and an international student. I love listening to Indie music, watching 80s movies, and reading in my spare time. I enjoy math because it allows me to express myself artistically, and tutor for the mere sake of those aha moments. I'm currently taking Calc 3 and AP Physics C, hope to see you soon!

### Upcoming Sessions

Session 3

#### Meetup

(Approx. 1h 30m)

The Sum of The Interior and Exterior Angles of N-Polygons (proofs and worksheets)

-Proof of the sum of interior angles for a triangle

-Proof and properties of parallelograms, rectangles, rhombuses.

(Properties: diagonals, side lengths, angle properties, and area)

Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 4

#### Meetup

(Approx. 1h)

-Complete review and practice from last session.

-Proof and properties of kites and trapezoids.

(Properties: diagonals, side lengths, angle properties, and area)

Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 5

#### Performing transformations

(Aprox 1h 30m)

Hey guys, today we will cover the Performing Transformations unit.

We will learn about what transformations are, their applications in real life, specifically

1. Rigid and non-rigid transformations

2. Translations, reflections, rotations, and...

3. Dilations Their functional notation and the relationships between various transformations. As always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 6

#### Transformation properties and proofs

(Aprox 1h 30m)

Hey guys,

today we will review transformation properties and start discussing proofs using transformations--which will be especially helpful when we get to congruence and similarity proofs. As always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 7

#### Similarity

(Aprox 1h 30m)

Hey everyone,

Today we will review non-rigid transformation (dilation) properties and will derive similarity theorems such as AA, AAA, and the angle bisector theorem. We'll also learn about ratios proportions, and how to solve basic rational equations. We'll use all of this to find the missing side lengths of figures. Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 8

#### Right triangles & trigonometry

Hey guys,

Today we will review the pythagorean theorem (which we proved using similarity last unit) and learn about it in 3 dimensions. We'll apply the formula in some practice questions and then move on to special right triangles (30-60-90 and 45-45-90 right triangles, to be specific). We will also introduce the idea of SOHCAHTOA to find the lengths of missing side lengths of right triangles. Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 9

#### Analytic geometry

(Approx 1h).

Hey guys, we're nearing the end but we still have some units left to go. Today we will discuss what is the coordinate plane, why it is important to understand it, and how to read it. We will also learn the distance formula, the midpoint formula, and how divide line segments. As always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 10

#### Circles

(Approx 1h15m).

Here we will cover Circle Properties and Theorems: what parts of the circles are called; how to calculate its area and sector areas; and how to calculate its circumference length, as well as arc lengths. We will also discuss circle theorems and prove them. As always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 11

#### Circles

(Approx 1h).

Hey guys,

Today we will finish discussing the properties of circles and applying them in practice problems. As always, if you need a catch-up/office-hours session, let me know!

Session 12

#### Meetup

(Approx 1h30m)

Hey guys, today we will briefly go on a tangent and learn quadratics.

We will

- Define Polynomials, Degree, Types of Polynomials, Leading Coefficient

-Define Polynomial Addition and Subtraction

-Define Polynomial Multiplication -Introduce the standard form of a quadratic (and explore its characteristics, i.e., its degree, number of terms etc.) -Introduce the notion of roots -Graph parabolas (quadratic expressions) to explore its characteristics (e.g., what happens when the leading coefficient is negative?) Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 13

#### Analytic geometry

(Aprox. 1h 30m)

-Introduce the notion of completing the square and practice doing so

-Introduce vertex form and convert the standard form of a quadratic expression into vertex form

-Use completing the square to convert the equation of a circle to its standard form.

Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 14

#### Analytic geometry

(Aprox. 1h 30m)

Hey guys, today we'll go over ellipses:

- The geometric definition and properties of ellipses

-Deriving the standard form of an ellipse

-Graphing ellipses given certain data (foci coordinates, axes lengths, etc.)

Session 15

#### Analytic geometry

(Aprox. 1h 30m)

Hey guys, today we'll go over hyperbolas:

- The geometric definition and properties of hyperbolas

-Deriving the standard form of a hyperbola

-Graphing hyperbolas given certain data (foci coordinates, axes lengths, etc.)

Session 16

#### Review

(Aprox. 1h15m)

Today we'll work on some Khan Academy questions regarding both ellipses and hyperbolas to practice and cement our knowledge!

Session 17

#### Analytic geometry

(Approx 1h30m).

Today we will move on to our final conic section: Parabolas!

By far the easiest, we will, once again...

-Define parabolas geometrically

-Derive the equation of a vertical and horizontal parabola given a focus and directrix

-Convert this to the equation of a parabola given the latus rectum or focal length Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 18

#### Analytic geometry

(Approx. 1h30m)

Today we'll work on some Khan Academy questions regarding parabolas.

After that, we will derive the equation of a general parabola (not only in the special cases that it is a vertical or horizontal one) by first deriving the equation for distance from a point to a line. Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.

Session 19

#### Meetup

(Approx 1h30m).

Circumcenter and circumcircles. (More info to be added soon!)

Session 20

#### Meetup

(Approx 1h30m).

Incenters and Incircles. (More info to be added soon!)

Session 21

#### Meetup

(Approx 1h30m).

Medians and Centroids. (More info to be added soon!)

Session 22

#### Meetup

(Approx 1h15m).

Orthocenters and Euler's Line. (More info to be added soon!)

Session 23

#### Meetup

Introduction to Vectors

-We will explore what an n-vector is, what a vectors space is

-What is and how to calculate and interpret magnitude

-Understand what vector components are and how to understand direction through them.

Session 24

#### Meetup

Introduction to Vector Operation

-We will explore what a unit and zero-vector are.

-We will define vector addition and subtraction

-We will define the dot product

-We will explore the law of cosines for vectors and define orthogonality

Session 25

#### Meetup

Defining planes parametrically and algebraically

-Define parametric equations

-Define the algebraic equation of a plane

-Using three points on a plane to find the parametric and algebraic equations of a plane, and convert between the two.

-Using a normal vector to find the algebraic and parametric equations of a plane.