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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.
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 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 Triangle
2. Classification by Sides
3. Classification by Angles
Section 4-1
Triangles and Angles
Pg. 194
Let’s add some more vocabulary:
How many Exterior angles are there in a Triangle?
How many Interior angles are there in a Triangle?
3 of each
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 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.
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. 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)
B
3
4
A
2
5
C
1
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 C P C T C stand for?
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 M  T , 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