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: vertices acute triangle obtuse triangle right triangle hypotenuse legs scalene triangle isosceles triangle equilateral equiangular vertex angle base 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 SketchesGeometer SketchPad Sketches 4.1

Section 4-1 Triangles and Angles Pg. 194 Now let’s arrange our vocab terms into three categories:let’s arrange 1. Names of parts of a Triangle 2. Classification by Sides 3. 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. 194 Conceptual 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 SketchesGeometer SketchPad Sketches 4.1 (cont.)

Section 4-2 Congruence and Triangles Pg. 202 CO: We will define Congruency of Triangles now. Triangles are congruent if their Corresponding Parts are CONGRUENT

Section 4-2 Congruence 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.GSP sketches.

Section 4-2 Congruence 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 And don’t forget to read the Theorems!

HOMEWORK Pg 198: #11-25 ODD, 31 – 39 ODD, 41, 43, 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)

Section 4-3 Proving Triangles are Congruent SSS and SAS Pg. 212 CO: Let’s take the first few minutes of class to read THE PARAGRAPH ABOVE the Theorems on pg. 205.

Section 4-3 Proving Triangles are Congruent SSS and SAS Pg. 212 CO: Explain what the author meant by “more efficient ways of proving that triangles are congruent”.

Section 4-3 Proving Triangles are Congruent SSS and SAS Pg. 212 DITI: Let’s take 10 minutes or so to read thru Section 4-3.

Section 4-3 Proving Triangles are Congruent SSS and SAS Practice: Pg. 216 #12-20, even

Section 4-4 Proving Triangles are Congruent ASA and AAS Pg. 220 DITI: Let’s take 10 minutes or so to read thru Section 4-4

Section 4-4 Proving Triangles are Congruent ASA and AAS Practice: Pg. 223 #8-18, even

Section 4-3/4-4 Tests 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 Side Test 2: SAS – Side Angle Side Test 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? PCCTC orrespondingarts ofongruentriangles areongruent

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!

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 4-6 Isosceles, Equilateral, and Right Triangles pg. 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