Math 20-2

Chapter 2 Properties of Angles and Triangles

Lesson 2.5 Exploring Congruent Triangles

GOAL

The goal of this lesson is stated at the top of page 104 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Determine the minimum amount of information needed to prove that two triangles are congruent.

Explore the Math

A chance to explore the ideas of the lesson

TEXT Page 104

Read/Work through the Explore the Math section on Page 104 in your textbook.

This is one of the most important ideas in geometry, and will form the basis of all the trigonometry we will be studying.

You are welcome to just “explore” the idea on your own!

However, since this is such an important idea,  the steps below provide a more GUIDED approach that you can follow.

Each of the video tutorials will provide information and direction,  to help you explore these ideas.

Lots of videos, but each one is SHORT, and will take you through these ideas, step by step, and encourage you to participate as you go.

You should have a RULER and a PROTRACTOR ready so you can DO these explorations.

VIdeo Tutorials

Congruence   vs.   Similarity     			Video Tutorial  (Part 1)

INTRODUCTION					Video Tutorial   (Part 2)

Minimum Information				Video Tutorial   (Part 3)

Just one angle						Video Tutorial    (Part 4)

Geometry Software (constraints)		Video Tutorial    (Part 5)

Just one side						Video Tutorial    (Part 6)

Two Angles...?						Video Tutorial    (Part 7)

Two Angles...?	(constraints)			Video Tutorial    (Part 8)

Two pieces of information?			Video Tutorial    (Part 9)

Counter-examples (two pieces of info)	Video Tutorial    (Part 10)

Three pieces of information?			Video Tutorial    (Part 11)

ASA								Video Tutorial

SAS								Video Tutorial

SSS								Video Tutorial

AAS								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!

Here is a collection of the 6 possible combinations of information and what they mean, and if they work.
Collections with an asterisk (*) will be the focus of this class.

*ASA is when we know two angles and a side between the angles.     YES, congruence is guaranteed
(but maybe doesn’t fit the definition of minimum, since we actually know FOUR pieces of information,  AA actually means AAA)

*SAS is when we know two sides and the angle between them.     YES, congruence is guaranteed

*SSS is when we know three sides of the triangle.       YES, congruence is guaranteed

*AAS is when we know two angles and one side (which is not between the angles).  YES, congruence is guaranteed
(but maybe doesn’t fit the definition of minimum, since we actually know FOUR pieces of information,  AA actually means AAA)

SSA is when we know two sides and an angle that is not the angle between the sides.     (maybe....)
(This is a tougher one and would possibly be explored in a future math class)

AAA  is when we know all three angles of a triangle, but no sides.   No,  congruence is NOT guaranteed

Print

Sorry, not a complete playlist of facts,  but a start.
You can print this an use it like a formula sheet (but check with your teacher about use on tests and quizzes, etc.

LINK
https://drive.google.com/file/d/1sfZFABPbRPCf0xfvIgtoBV-dgJA6ij-M/view?usp=sharing

Further Your Understanding

Further Your Understanding problems reinforce the math presented in this lesson.

These are just practice problems with a different heading....

•	Work through these 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!

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"}})