Geometry • Series
High School Geometry and Introductory Linear Algebra
PL
JG
Jose Roberto Cossich G
This series was cancelled by the tutor on May 25, 2023. We're very sorry–you can explore more Geometry series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.
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 25
Learners
99 / 100
Total Sessions
23
About the Tutor
PL
JG
A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.
View Jose Roberto Cossich G's Profile
Upcoming Sessions
0
Past Sessions
23
13
Nov
OT
Session 1
Other Topics
(Approx. 1h15m + 15m for Orientation)
Hey guys,
Today we will be covering the Lines and Angle units on Khan Academy. We will cover the following:
1. Definitions of points, rays, lines, line segments, and angles
2. Basic definitions of parallel and perpendicular lines
3. Vertical, complementary, and supplementary angles
4. Angle theorems having to do with parallel lines.
This will be very important as we begin our journey to learn geometry. If you cannot make it to this session (or have to join late/leave early please send me a private chat--I will do my best to set up a catch-up session. Like any other branch of math, geometry is foundational and we cannot move on to more advanced topics until we have mastered the basics.
Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.
20
Nov
OT
Session 2
Other Topics
(Approx. 1h15m)
Hey guys!
Today we will be moving on to classifying general shapes and triangle types. We will also apply and prove the Triangle Inequality Theorem, and discuss angle and segment bisectors and altitudes. After that, we will introduce polygons and their classifications. Hope to see you then, and again, if you can't make it, feel free to private message me to do a catch-up session.
5
Dec
OT
Session 3
Other Topics
(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.
11
Dec
OT
Session 4
Other Topics
(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.
18
Dec
Pt
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.
28
Dec
Tp
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.
15
Jan
S
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.
21
Jan
Rt
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.
22
Jan
C
Session 9
Congruence
Here we will cover congruence theorems, specifically SSS, SAS, AAS, and RHS, as well as incomplete congruence theorems such as SSA. We will also apply these congruence theorems in finding the properties of polygons, proving what we had previously just assumed. As always, feel free to ask for a catch-up/office our session in the group/private chat.
28
Jan
Ag
Session 10
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.
29
Jan
C
Session 11
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.
6
Feb
C
Session 12
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!
12
Feb
OT
Session 13
Other Topics
(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.
20
Feb
Ag
Session 14
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.
28
Feb
Ag
Session 15
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.)
Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.
5
Mar
Ag
Session 16
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.)
Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.
12
Mar
R
Session 17
Review
(Aprox. 1h15m)
Today we'll work on some Khan Academy questions regarding both ellipses and hyperbolas to practice and cement our knowledge!
Hope to see you there, and as always, feel free to ask for a catch-up/office our session in the group/private chat.
19
Mar
Ag
Session 18
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.
27
Mar
Ag
Session 19
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.
15
Apr
OT
Session 20
Other Topics
(Approx 1h30m).
Circumcenter and circumcircles. (More info to be added soon!)
16
Apr
OT
Session 21
Other Topics
(Approx 1h30m).
Incenters and Incircles. (More info to be added soon!)
24
May
OT
Session 22
Other Topics
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.
25
May
OT
Session 23
Other Topics
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