研究幾何第 2 部分（共 5 部分）

In this second part of high school geometry, we will investigate triangles and their congruence along with Quadrilaterals and polygons. We will also review area of these shapes. (3 times a week for 8 weeks).
In each of these parts your child will be taught the skill and then asked to apply the skill in a discovery lesson. Skill learning will be circular within each part. Meaning a skill that you learned in Part 1 will be retaught with further learning in another part. Below is a breakdown of what you will see in this class.
In this class we will be working with Tools of Geometry, and reasoning and proof. Be sure to check the supply list to ensure you have all the required tools so that your learner can model the different concepts.
In this class learner will be done through in class examples, group investigations, worksheets, quizzes, and projects.
Objectives for this course: 
Prove theorems about triangles. Theorems include: Measure of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Prove theorems about parallelograms. Theorems include opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar.
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Before this class, your learner should have taken Pre-algebra and Algebra one curriculum. If you are unsure of what curriculum to put your learner in, please check out my Math Evaluation class first: https://outschool.com/classes/math-evaluation-QSjWiJt4?usid=MoqFvLdS&signup=true&utm_campaign=share_activity_link


Breakdown of topics (Subject to change)
Week one: Types of triangles and their angles
Week two and three: Triangle Congruence
Week four: Triangle bisectors and Inequalities
Week five and six: Quadrilaterals and polygons
Week Seven: Angle measures in polygons
Week eight: Graphing polygons
 
Grading is available upon request. There will be 4 quizzes and 2 projects in this class that can be graded.
A geometry set is required for this class. Any set that has the following items will do:
Patty paper  ( https://www.amazon.com/UltraSource-192033-Hamburger-Patty-Paper/dp/B00TDBVW7W/ref=cm_cr_arp_d_pb_opt?ie=UTF8 )
A ruler (12 inches and 30 cm)
A protractor
A compass
Geo board or printable supplied in class
Graph paper (printable supplied in class)
Here is an example on amazon: https://www.amazon.com/gp/product/B0745Z3RTZ/ref=ox_sc_act_title_1?smid=A1YMG5SVGVCW58&psc=1
Your learner will also need a notebook to write in (this can be the same one started in Part One). Geometry has its own set of vocabulary and learning it can be like learning a new language. Students will have a set of vocabulary they must put in their geometry dictionary (notebook) each week.

I like to show the students the way math rules work so that it is easier to remember them. This way the curiosity of knowing how something works will move the gears of critical thinking. After I have shown them a pattern and why it works. I will ask them to apply it to a hard problem. If they can use these skills in diverse ways, I know they have mastered the concepts. I believe to memorize math is not understanding, but to apply math is not only understanding but fluency! To obtain this level of understanding, I will lead the students on a journey to discovering math through discussion, observation, and application of the math being used. If this is the kind of math class, you want then I am the teacher for you. 

I am a homeschooler, and I enjoy the freedom of figuring out how my child is assessed. I will give suggested practice problems each class and provide homework videos. Whether or not the practice problems are mandatory and graded is up to the parent. I will give in-class assignments such as discovery labs and discussion word problems. If you want an assignment done on your learner at the end of class, it will be the job of the parent to contact me within the first week of class so that I can send them my due dates for assessment work.