Download Chapter 4 Notes_Updated - Kenwood Academy High School

Chapter 4: Congruent Triangles
4.1 Classifying OBJECTIVES: Students will be able to
Triangles * identify and classify triangles by angles
* identify and classify triangles by sides
Why is important to learn Triangles in construction:
about triangles?
___________________________________________________________
Triangle Label
Sketch an example
Types of Triangles: Acute – all angles are acute
Classify by Angles
There are 3 types of angles:
Obtuse – one angle is obtuse
Acute:
Obtuse:
Right – one angle is right
Right:
What is the symbol used to
show that angles are
congruent?
Classify by Sides
What is the symbol used to
show that line segments are
congruent?
Equiangular – all angles are
equal
Scalene – no two sides are
congruent
Isosceles – at least two sides
are congruent
Equilateral –all sides are
congruent
Examples
Identify the indicated type of triangles if
AB  AD  BD  DC , BE  ED, AB  BC and ED  DC .
Day 1 Homework:
Assignment 4.1 page 180
(3-4, 9-10, 22-25, 48, 50)
1. right
2. obtuse
3. scalene
4. isosceles
Use the B/D/A Strategy Find x and the measure of each side of the triangle.
5. Triangle FGH is equilateral. FG = x + 5, GH = 3x - 9, and FH = 2x - 2.
Underline
Draw
Underline (Key Words & Numbers):
Find
Choose
Draw (don’t forget to label):
Find (what the problem is asking):
Solve
Choose (how are you going to solve? Set up to solve) & Solve:
CHECK: does your answer make sense? Do you have everything you needed to
answer the problem?
6. Triangle LMN is isosceles, L is the vertex angle, LM = 3x - 2,
LN = 2x + 1, and MN = 5x - 2.
Use the distance formula In problems 7 & 8, find the measures of the sides of triangle KPL and
classify each triangle by its sides.
7. K(-3, 2) P(2, 1), L(-2, -3)
Distance formula review:
The distance, d, between points
𝑥�1�, 𝑦�1�� and
𝑥�2�, 𝑦�2�� is
How to solve problems like this?
8. K(5, -3), P(3, 4), L(-1, 1)
Day 2 Homework:
Assignment 4.1 page 180
(26-29, 33-37 odd, 46, 49)
4.3 Congruent Triangles Objective:
-Name and label corresponding parts of congruent triangles
Why does order matter?: What would happen if you put your shoes on before your pants?
Definition of  Triangles
CPCTC
Naming  corresponding a.
parts
**The vertices of the triangles
correspond in the same order
as the letters naming the
triangles.
A  ______
B ______
F ______
AC  ______
DE  ______
FE  ______
b.
∆ABD  ∆CBD
If two triangles are congruent, you can slide, flip, or turn one of the
triangles and they will still be congruent. These are called congruence
transformations because they do not change the size or shape of the
figure.
Assignment 4.3 page 195
#9-16, 29-32,38,39
4.4 and 4.5 Proving Objective:
Congruence – SSS, SAS, -Use the SSS, SAS, ASA, and AAS Postulate to test for triangle
ASA, AAS congruence.
Postulates that Prove
Triangles Congruent:
(shortcuts to proving
triangles congruent)
Using The Postulates:
1. Suppose D is the midpoint of both GE and FH. Label the pictures
first. Then decide, if you are
given enough information to prove the triangles are congruent? Explain
2. How would you complete the following congruence statement?
▲FDE __________
3. Suppose you are not told anything about D but instead you are told
that GH║FE. Can you prove the triangles above are congruent? Explain.
4. This time, suppose you know that EF GH and EF║ GH. Can you
prove the two triangles above are congruent? Explain.
5. In this diagram, D is the midpoint of AC and AB CB. First label the
picture. Then decide if you can prove any triangles congruent? Explain.
Proving Triangles 
Examples:
1. Given: X is the midpoint of FM
; OF AM; OX AX .
Prove: ΔFOX ΔMAX
2.
First label the pictures with the given information. Then ask your self if
you have enough information to prove the triangles using SSS, SAS,
ASA, AAS
Statements
Reasons
Statements
Reasons
3.
Statements
Reasons
4.
Statements
Assignment 4.4 & 4.5
Part 1: page 203 #7-11,
Part 2:page 203 #6,16
page 210 #6,9,10,15
Reasons
4.6 Isosceles Triangles Objective:-use properties of isosceles triangles
-use properties of equilateral triangles
Properties of Isosceles
Triangles
Vertex Angle: ______
legs:_____________
Definition of an Isosceles Triangle:___
_________________________________
_________________________________
_________________________________
Base Angles:_____________
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite
those sides are congruent.
Example: Find x.
Converse Isosceles Triangle If two angles of a triangle are congruent, then the sides opposite
Theorem those angles are congruent.
Example: Find x.
Equilateral Triangles
Draw an Equilateral Triangle
Compare the isosceles and
Equilateral Triangles
List all properties
True or false.
All Equilateral triangles are
Isosceles._______________________
Assignment A triangle is equilateral if and only if it is
page 219 #6,8-28, 35,36 equiangular.__________
All Isosceles triangles are Equilateral___________________
Each angle of an equilateral triangle measures
60°.____________