### SSS - Ms. Huls

```Happy Monday 
Do Before the Bell Rings:
1. Pick up the papers from the front table.
pen.
3. Take out your whiteboard and whiteboard pens.
Math History Presentations will be due tomorrow!
3 Things
Do Now!: Whiteboards
1. Find mABD.
1. ∆PQR  ∆STW Name all pairs of congruent corresponding
parts.
1. Angles: P  S, Q  T, R  W
2. Sides: PQ  ST, QR  TW, PR  SW
Whiteboards
3. Name a congruence statement for the following figure.
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.
Math Joke of the Day
• What do you call a fierce beast?
• A line
On Friday…
• You proved triangles are congruent by
showing that all six pairs of corresponding
pairs were congruent.
• Today, we are learning a shortcut!
4-4 Triangle Congruence: SSS and SAS
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
Example 1:
(a) Use SSS to explain why ∆ABC  ∆DBC.
It is given that AC  DC and that AB  DB. By the
Reflexive Property of Congruence, BC  BC.
Therefore ∆ABC  ∆DBC by SSS.
Example #1
b) Use SSS to explain why
∆ABC  ∆CDA.
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:CFU
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 2:
(a) Use SAS to explain why ∆XYZ  ∆VWZ.
It is given that XZ  VZ and that YZ  WZ. By the Vertical
s Theorem. XZY  VZW. Therefore ∆XYZ  ∆VWZ by
SAS.
Whiteboards
Use SAS to explain why ∆ABC  ∆DBC.
It is given that BA  BD and ABC  DBC. By
the Reflexive Property of , BC  BC. So ∆ABC 
∆DBC by SAS.
Example 3: 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.
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.
p. 245: #1-7
If you get stuck: