Happy Wednesday!
 Pick up notes and take out homework
Tonight’s HW:
1. P 227 #12-14
2. P 234 #1-11
3. P 245 # 1-7
4. Make notecards from U2L7 and U2L8 (definition one side and
vocab. word on the other side
 Updates:
o Unit 2 Quiz 2 (4.1-4.4)
Monday 10/27
Agenda
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Review HW/ Warm- Up!
Notecard War!
Finish 4.2
4.3: Congruent Triangles
4.4: Triangle Congruence: SSS and SAS
Cool-Down…
Stamping
I am going to stamp your homework and the worksheet on the back
of your 4.1 notes.
HAVE IT OUT AND READY! If it is not out on your desk when I come
by, you will NOT get a STAMP!
While I am doing this , you are going to be doing whiteboards. If I
come around and you are NOT working on whiteboards, you will be
docked participation points.
Stamping
I am going to stamp your homework and the worksheet on the back
of your 4.1 notes.
HAVE IT OUT AND READY! If it is not out on your desk when I come
by, you will NOT get a STAMP!
While I am doing this , you are going to be doing whiteboards. If I
come around and you are NOT working on whiteboards, you will be
docked participation points.
Whiteboards
Find mACD.
Whiteboards
After an accident, the positions of cars are
measured by law enforcement to
investigate the collision. Use the diagram
drawn from the information collected to
find the following:
1. mXYZ.
2. mYWZ
Review HW (p 219 #1-11)
2. One of the angles is obtuse and the other two angles are acute
4.Right
6. Isosceles
8. Scalene
10. 3.1. 3.1, 3.3
Review HW (p 227 # 4-11, 24)
4. 17
6. 69.2
8. 65 1/3
10. 41
24) a. Given,
b. m <F= 90
c. Triangle Sum Theorem
d. Substitution
e. m<D +m<E= 90
f. Def of complementary
angles
Review HW (Worksheet on back
of 4.1)
On Doc Cam
How do we Use Notecards
Effectively?
Any ideas?
You are going to pair up with someone at your table. Person 1 will
go first and show your partner your vocab word.
Person 2 will say everything they know about the vocab word. You
will go through your deck until you are done.
Then SWITCH!
Keep doing this until you get the entire pile of notecards CORRECT!
How do we Use Notecards
Effectively?
We will do this every block period since this Unit is a lot of
vocab 
4.2 Continued…
We did not finish 4.2 note so please take them out 
Third Angle Theorem
Example 4: Applying the Third Angle
Theorem
Find mK and mJ.
Whiteboards
Find mP and mT.
Learning Objective(s)
By the end of this period you will be able to:
① Use properties of congruent triangles
② Apply SSS and SAS to construct triangles and to solve problems
Congruent Triangles
Corresponding angles and corresponding sides
– Same position in polygons with an equal number of
sides
Congruent Polygons
o If corresponding sides are congruent
Congruent Triangles
Congruent Triangles
• triangles that are the same shape and size.
• Two triangles are congruent if and only if their
corresponding parts are congruent .
• Corresponding angles and corresponding sides
are in the same position in the triangle
• Name congruent triangles using Congruence
Statements. Congruence Statements orders the
vertices based on the congruent parts.
• ORDER MATTERS!
Congruent Triangles
Congruence Statement:
Corresponding Congruent Angles:
Corresponding Congruent Sides:
EX 1: Naming Congruent
Corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent
parts.
Angles: P  S, Q  T, R  W
Sides: PQ  ST, QR  TW, PR  SW
Example 1 (b)
Example 2: Using Corresponding Parts
of Congruent Triangles
Given: ∆ABC  ∆DBC.
1. Find the value of x.
2. Find mDBC.
Whiteboards
Given: ∆ABC  ∆DEF
1. Find the value of x..
2. Find mF.
Example 3
Whiteboards
Do the following problem on your whiteboard
individually.
∆ABC  ∆JKL and AB = 2x + 12.
JK = 4x – 50. Find x and AB.
Whiteboard Activity
Find another student in the room. You must choose a student who
has:
(1) A name starting with the same letter as yours OR
(2) A last name starting with the same letter as yours.
These people CANNOT be at your table!
You will be checking your partners work. If the students see a
mistake in your work they are to help correct your mistake.
Whiteboards
Do the following problem on your whiteboard individually.
1. Given that polygon MNOP  polygon
QRST, identify the congruent
corresponding part.
• a. NO  ____
b. T  ____
Whiteboard Activity
Find another student in the room ( who you did not choose for #1).
You must choose a student who has:
(1) A name starting with the same letter as yours OR
(2) A last name starting with the same letter as yours.
These people CANNOT be at your table!
You will be checking your partners work. If the students see a
mistake in your work they are to help correct your mistake.
Math Joke of the Day
• What do you call a fierce beast?
• A line
4.4: Triangle Congruence: SSS and SAS
Learning Objective
SWBAT apply SSS and SAS to show triangles
are congruent.
SWBAT prove triangles are congruent by using
SSS and SAS.
SSS and SAS Congruence (4.4)
Instead of having to prove that all sides and angles are congruent in
order to prove that triangles are congruent, we are going to learn 5
shortcuts.
There are five ways to prove triangles are congruent:
1. SSS
2. SAS
3. ASA
4. AAS
5. HL
Today we are going to discuss SSS and SAS.
4-4 Triangle Congruence: SSS and SAS
Side–Side–Side Congruence (SSS)
• If the sides of one triangle are congruent to the sides of a
second triangle, then the triangles are congruent.
• We abbreviate Side-Side-Side Congruence as SSS.
What is a possible congruent statement for the figures?
• Examples
• Non-Examples
4-4 Triangle Congruence: SSS and SAS
Included Angle
• An angle formed by two adjacent
sides of a polygon.
• B is the included angle between
sides AB and BC.
Whiteboards
1. What is the included
angle between the
sides BC and CA?
2. What are the sides of
the included angle A?
Side-Angle-Side Congruence
Side–Angle–Side Congruence (SAS)
• If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another
triangle, then the triangles are congruent.
What is the possible congruence statement for the figures?
Example/ Non-Examples
• Example
• Non-Example
4-4 Triangle Congruence: SSS and SAS
Example 1:
(a) Use SSS to explain why ∆ABC  ∆DBC.
Use the following sentence frame:
It is given that ____  ____ and __  ______
By the ___________________________,
____ _____. Therefore ________  _________ by
________
Whiteboards
Explain why ∆ABC  ∆CDA.
It is given that ____  ____ and __  ______
By the ___________ ____________ of Congruence,
____ _____. Therefore ________  _________
by ________
4-4 Triangle Congruence: SSS and SAS
Example 1(b) :
Explain why ∆XYZ  ∆VWZ.
It is given that ____  ____ and __  ______
By the __________________________________________,
____ _____. Therefore ________  _________ by
________
Whiteboards
Explain why ∆ABC  ∆DBC.
I am not going to to give you the
sentence frame, but I still want you to use complete
sentences. Follow what you have on your notes.
It is given that BA  BD and ABC  DBC. By
the Reflexive Property of , BC  BC. So ∆ABC 
∆DBC by SAS.
Example 2: Verifying Triangle Congruence
Show that the triangles are congruent for the given value of the
variable.
∆MNO  ∆PQR, when x = 5.
PQ  MN, QR  NO, PR  MO
∆MNO  ∆PQR by SSS.
Whiteboards
Show that the triangles are congruent for the given value of the
variable.
∆STU  ∆VWX, when y = 4.
ST  VW, TU  WX, and T  W.
∆STU  ∆VWX by SAS.
4-4 Triangle Congruence: SSS and SAS
Example 3:
The Hatfield and McCoy families are feuding over some land.
Neither family will be satisfied unless the two triangular fields
are exactly the same size. You know that BC is parallel to AD
and the midpoint of each of the intersecting segments. Write
a two-column proof that will settle the dispute.
. Given: BC || AD, BC  AD
Prove: ∆ABC  ∆CDB
Proof:
Closure Questions
Which postulate, if any, can be used to prove the triangles
congruent? In one sentence tell why or why not the triangles
are congruent.
1.
2.
Begin Homework
For the remaining time please begin the homework.
If you get stuck:
1. Talk to your tablemates.
2. If all of your tablemates are confused raise your hand and
I will assist you as soon as I can.