Chapter 4 Congruent Triangles

Pg. 191

Conceptual Objective (CO):

We will now begin to explore Triangles. We will classify them and determine (thru proofs) whether two triangles are Congruent.

Chapter 4 Congruent Triangles

Pg. 191

Conceptual Objective (CO):

Congruent triangles have all the same side lengths and all the same angle measurements.

In this chapter there is a lot of new vocabulary and so I strongly suggest you start a CH 4 dictionary and as you see new words you write them in your dictionary.

Section 4-1 Triangles and Angles

Pg. 194

Let’s start with some vocabulary:

verticesacute triangle

obtuse triangleright triangle

hypotenuselegs

scalene triangleisosceles triangle

equilateralequiangular

vertex anglebase angles

Section 4-1 Triangles and Angles

Pg. 194

Conceptual Objective (CO): We will identify parts of the triangle and classify triangles.

DITI: Let’s look at some nice Geometer SketchPad Sketches

4.1

Section 4-1 Triangles and Angles

Pg. 194

Now let’s arrange our vocab terms into three categories: 1. Names of parts of a Triangle2. Classification by Sides3. Classification by Angles

Let’s add some more vocabulary:

Section 4-1 Triangles and Angles

Pg. 194

Exterior Angle

How many Exterior angles are there in a Triangle?How many Interior angles are there in a Triangle?

3 of each

Interior Angle

Section 4-1 Triangles and Angles

Pg. 194Conceptual Objective (CO):

We will understand the facts and relationships between and among the angles in a triangle.

DITI: Let’s look at some nice Geometer SketchPad Sketches

4.1 (cont.)

Section 4-2Congruence and Triangles

Pg. 202

CO: We will define Congruency of Triangles now.

Triangles are congruent if their

Corresponding Parts are CONGRUENTCorresponding Parts are CONGRUENT

Section 4-2Congruence and Triangles

Pg. 202

DITI: In order to understand Triangle congruency we

need to consider Corresponding Parts.

Let’s look at some more GSP sketches.

Section 4-2Congruence and Triangles

Pg. 202

DITI: Let’s take the last few minutes of class to read thru Section 4-2.

PAY CLOSE ATTENTION TO THE PARAGRAPH ABOVE the Theorems on pg. 205. And don’t forget to read the Theorems!

HOMEWORK

Pg 198: #11-25 ODD, 31 – 39 ODD, 41, 43, 45 - 47

Pg 206: #10 – 15, 17 – 29 ODD, 35, 38

WARM UP

Given the following diagram and if the measure of Angle 3 is 105º, find the measure of Angle 2.

(RECALL: The base angles of an isosceles triangle are congruent)

3

15

4

2A

B

C

Section 4-3Proving Triangles are Congruent

SSS and SASPg. 212

CO: Let’s take the first few minutes of class to read THE PARAGRAPH ABOVE the Theorems on pg. 205.

Section 4-3Proving Triangles are Congruent

SSS and SASPg. 212

CO:

Explain what the author meant by “more efficient ways of proving that triangles are congruent”.

Section 4-3Proving Triangles are Congruent

SSS and SASPg. 212

DITI: Let’s take 10 minutes or so to read thru Section 4-3.

Section 4-3Proving Triangles are Congruent

SSS and SAS

Practice: Pg. 216 #12-20, even

Section 4-4 Proving Triangles are Congruent

ASA and AASPg. 220

DITI: Let’s take 10 minutes or so to read thru Section 4-4

Section 4-4Proving Triangles are Congruent

ASA and AAS

Practice: Pg. 223 #8-18, even

Section 4-3/4-4Tests for Congruent Triangles

There are four tests for congruency: if two Triangles pass any of the four tests, then they are Congruent!

Test 1: SSS – Side Side SideTest 2: SAS – Side Angle SideTest 3: ASA – Angle Side Angle Test 4: AAS – Angle Angle Side

HOMEWORK 4-3/4-4

Pg 216: #7-23 ODD

Pg 223: #9-23 ODD

Section 4-5 Using Congruent

Triangles Pg. 229

CO: In this section we

FIRST prove triangles congruent using three parts (ASA, SSS, AAS, SAS)

THEN we use CPCTC to prove that other parts of the triangles are congruent.

What does stand for? P CC T C

orresponding arts of ongruent riangles are ongruent

Section 4-5 Using Congruent

Triangles Pg. 229

DITI: The only way to learn this is to practice! So…right now first read Ex 1. (OH BY THE WAY…this teaches you some general strategies for doing proofs…so pay attention!)

Then read Ex 2. Notice this actually has you FIRST prove triangles congruent using three parts (SAS), THEN use CPCTC to prove that , and THEN finally prove the actual Prove statement with the AIA Converse. Now we’re talking!

Then read Ex #3. How cool!

M T

Section 4-5 Using Congruent

Triangles Pg. 229

DITI: I hope you have noticed that our proofs are getting more complicated. We now realize we may have to prove some intermediary results before we can get to our actual Prove Statement. So be ready for it!

Section 4-6Isosceles, Equilateral, and Right

Trianglespg. 236

CO: Here is where the book finally states some facts we already know.

But let’s talk about Theorem 4.8.

HOMEWORK 4-5 – 4-6

Pg. 232: #1-3, 8 – 10, 14, 15, 17 Pg. 239: #1-15 ODD, 33

Review Triangle Congruency

GSP sketches