chapter 4 congruent triangles pg. 191 conceptual objective (co): we will now begin to explore...
TRANSCRIPT
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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.
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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.
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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
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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
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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
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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
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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.)
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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
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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.
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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!
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HOMEWORK
Pg 198: #11-25 ODD, 31 – 39 ODD, 41, 43, 45 - 47
Pg 206: #10 – 15, 17 – 29 ODD, 35, 38
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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
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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.
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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”.
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Section 4-3Proving Triangles are Congruent
SSS and SASPg. 212
DITI: Let’s take 10 minutes or so to read thru Section 4-3.
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Section 4-3Proving Triangles are Congruent
SSS and SAS
Practice: Pg. 216 #12-20, even
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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
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Section 4-4Proving Triangles are Congruent
ASA and AAS
Practice: Pg. 223 #8-18, even
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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
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HOMEWORK 4-3/4-4
Pg 216: #7-23 ODD
Pg 223: #9-23 ODD
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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
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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
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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!
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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.
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HOMEWORK 4-5 – 4-6
Pg. 232: #1-3, 8 – 10, 14, 15, 17 Pg. 239: #1-15 ODD, 33
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Review Triangle Congruency
GSP sketches