Geometry • Series
Geometry and Trigonometry: Beginner to Advanced
PL
JG
Jose Roberto Cossich G
This series ended on December 30, 2021. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
Hey guys,
Since there was much demand for my original series on high school geometry, I decided to make a new, comprehensive series on Geometry, from the very basics to advanced trigonometry.
IMPORTANT: You can join this series AFTER it has begun in case there are any specific topics you would like to learn or review!
As I said, in this series we will covering all Khan Academy Courses on Basic Geometry, High School Geometry, and Trigonometry.
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, Right angles and trigonometry, Advanced Trigonometry, Analytical Geometry, Conic Sections, Circles, and Solid Geometry.
This series is for students who have already completed Prealgebra and Arithmetic and are eager to learn! This series is also intended for learners who learn better through conversation and discussion rather than idle videos.
✋ ATTENDANCE POLICY
Please do not miss any sessions before letting me know; remember that we can accommodate the time of each session--if not there will be make-up sessions depending on if anyone needs any. That being said, attendance for each session is not mandatory.
Dates
October 16 - December 30
Learners
38 / 40
Total Sessions
25
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
25
16
Oct
O
Session 1
Orientation
We'll go over what the series is about and what it will teach, what the expectations for both learners and students are, and finally we'll have fun and get to know each other!
17
Oct
Gf
Session 2
Geometry foundations
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. Anyways, thanks for joining the series and I hope to see you soon!
18
Oct
Gf
Session 3
Geometry foundations
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 (perpendicular) bisectors, centroids, medians, and altitudes. 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.
20
Oct
C
Session 4
Catchup
Hey guys! Today's going to be a catch-up for last session's content.
We'll be looking at how to classify general shapes and triangle types. We will also apply and prove the Triangle Inequality Theorem, and discuss angle (perpendicular) bisectors, centroids, medians, and altitudes.
23
Oct
C
Session 5
Catchup
Hey guys, today we will be having a catch-up session for those who weren't here for Geometric Constructions, the session we had last Saturday. Hope to see you there!
24
Oct
Ap
Session 6
Area and perimeter
Hey guys,
Today we will learn about various types of polygons and polygons, their properties, (as well as prove them), and how to find their area and perimeter.
25
Oct
Va
Session 7
Volume and surface area
Hey guys,
Last session we learnt about polygons, their properties, how to find their areas and perimeters. Today we'll be talking about 3D geometry, Cavalieri's Principle, and how to find the volume and surface area of 3D shapes. Hope you're looking forward to it and I hope to see you there! As always, feel free to ask for a catch-up/office our session in the group/private chat.
30
Oct
C
Session 8
Catchup
Hey guys, we're going to be doing a catch-up for last session. Hope to see you there!
31
Oct
Pt
Session 9
Performing transformations
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.
1
Nov
Pt
Session 10
Performing transformations
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.
3
Nov
Pt
Session 11
Performing transformations
Hey guys, today we'll be looking at function transformations.
Hope to see you there!
7
Nov
C
Session 12
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.
8
Nov
S
Session 13
Similarity
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. All of this will be particularly important as we enter our next unit which is on Trigonometry.
14
Nov
Rt
Session 14
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.
17
Nov
Rt
Session 15
Right triangles & trigonometry
Hey guys,
Today we will learn and prove the law of sines, cosines, and apply them to solve for the sides and angles of arbitrary triangles. We will also start talking about unit circles and their importance in trigonometry. As always, feel free to ask for a catch-up/office our session in the group/private chat.
21
Nov
T
Session 16
Trigonometry
Hey guys,
Today we will continue our discussion on the unit circle, talk about the domain and range of cosine, sine, and tangent functions and graph them. We will learn how to describe sinusoidal graphs (in terms of their amplitude, period, midline) and how to derive the equation which models a sinusoidal graph (without phase shift). We will also learn about the law of sines, prove it, and practice applying it.
22
Nov
T
Session 17
Trigonometry
Hey guys,
Today we'll be learning starting off by learning the law of cosines and applying it. Then, we'll learn how to write sinusoidal equations using information given in word problems. Afterwards we'll cover trigonometric identities (and their proofs). We'll also learn how to solve trig equations. This is by far the hardest unit we're covering this series, but remember, you're always free to ask for a catch-up/office our session in the group/private chat. Hope to see you soon!
28
Nov
T
Session 18
Trigonometry
We're going to be going over how to solve sinusoidal functions today, and some trig identities.
29
Nov
T
Session 19
Trigonometry
We're going to be going over trig identities, sum of angles and half-angles formulas. We will prove them and practice them using Khan Academy.
5
Dec
Ag
Session 20
Analytic geometry
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.
6
Dec
C
Session 21
Circles
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.
19
Dec
C
Session 22
Circles
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!
26
Dec
Gc
Session 23
Geometric constructions
Hey guys,
Today we will be deriving the equations of the next two conic sections using their standard equations, and vice versa. As always, feel free to ask for a catch-up/office-hours session if you need one!
27
Dec
Cs
Session 24
Conic sections
Today we'll go over parabola and ellipse constructions, their equations and proofs. It's the second to last session--good job guys!
30
Dec
R
Session 25
Review
Hey guys,
We'll be finishing going over ellipse equations and then go over hyperbola equations and proofs. After that, it's been absolutely great having you guys. Today we'll be reviewing what we've learnt, and we'll also do a quiziz on the series material to see who gets it best! We'll also be looking at the essays and presentations that you guys have made!