check YT 1,2  and PP 20, 21   add links  (revise links)

Math 20-2

Chapter 2 Properties of Angles and Triangles

Lesson 2.2 Angles Formed by Parallel Lines

GOAL

The goal of this lesson is stated at the top of page 73 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Prove properties of angles formed by parallel lines and a transversal, and use these properties to solve problems.

Geometry Facts

The link below is for a Geometry Facts document you can download and use in your math class.
You could print it, though it has been created to be viewed on computer.
Your teacher will have the final word,  but the idea is that you can use this document just like a formula/reference page for any work you do in  your class.
If you have ideas to make it more useful, let your teacher know, and the document can be edited accordingly!
LINK
https://drive.google.com/file/d/1Ub6rjs6KJo91tNInkbeuv_gugZy64_4G/view?usp=sharing

Video Tutorial

Proofs

In this chapter you are considering the question, “How do you know something is true?”

In mathematics, two different types of reasoning are used:

Inductive reasoning is the process of examining many examples, noticing a pattern, and stating a conjecture.

Deductive reasoning is the process of starting with statements assumed or accepted as true (generally from a previous sequence of deductive reasoning), 
then creating a logical sequence of statements 
(if a is true, then b is true; if b is true, then c is true; if c is true, then d is true, etc.), until we arrive at the desired conclusion.

Deductive geometry is the art of deriving new geometric facts from previously-known facts by using logical reasoning.

In previous math classes, many geometric facts were introduced by folding, cutting, or measuring exercises, not by logical deduction.
(inductive proofs)

In this chapter, you will be asked to do many formal proofs.

This is a challenging process.

To help with the process,  you can use the geometry facts document to support the steps of your proofs.
(this will depend on if your teacher allows you to use it...)

There are MANY MANY MANY facts that could go on this sheet!

I’ve limited the information to what I think you will need to use in this course.

If there is something you want to be included in the document, LET ME KNOW!

The document is a work in progress and I will happily revise it to make it more useful to you.

This will give you a set of FACTS that you know you can use, things we can assume are true.

Some things may be repeated if they are useful in more than one place.

You are welcome to print this document, but it’s been formatted more for reading on your computer.

Just keep it open on your computer screen so it is handy as you are doing your work

You are welcome to use abbreviations as long as it’s clear and your teacher can follow!

Explore...

Try to answer the question in the sidebar on page 73.

Watch

Video Tutorial

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 73 - 74

Read/Work through the Investigate section on Pages 73-74 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

Introduction

Video Tutorial

?  How can Briony use a straight edge and a compass to ensure that the lines she draws really are parallel?

Be sure to work through the investigation as best as you can, before you watch the video!!

If you like, you can try to use the online construction tools HERE  (but a physical compass and straight-edge will be easier!)

Video Tutorial

Reflecting

I covered these questions in the video from the previous section.

Apply the Math  (Examples)

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the examples as models.

Example 1  Reasoning about conjectures involving angles formed by transversals

TEXT Pages 75 - 76

Work through Example 1 on Pages 75 - 76 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Using reasoning to determine unknown angles

TEXT Page 76

Work through Example 2 on Page 76  in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Using angle properties to prove that lines are parallel

TEXT Page 77

Work through Example 3 on Page 77 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

In Summary

Key Ideas and Need to Know 
Presents and summarizes  the main new concepts of the lesson

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Practice Problems

USE FACT SHEET

REDO 12, 13, 16,  18. 19

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 7,    I didn’t do a video for this one.

Question 11,    I didn’t do a video for this one.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6",  , "Question 8", "Question 9", "Question 10"}, { ,  Question 12, Question 13 , "Question 14", "Question 15"}, {Question 16 , "Question 17", "Question 18", "Question 19", "Question 20"}, {"Question 21", , , , }})