1. GO GIANTS!
Pick up notes and the Exploration Activity
Tonight’s HW:
P 245 # 1-7
P 256 #1-8
Make notecards from U2L8 and U2L10 (definition one side and vocab. word on the other side

2. Agenda Review Transformation Test Exploration Activity!
4.4: SSS and SAS
4.5: AAS ASA HL
Proof Practice!
Stand Up!

3. Transformation Test Results
Overall, I am very proud of each and everyone of you for putting your best effort into the test.
1st Period
Average 27.1 out of 34
80%
6th Period
Average 28.7 out of 31
84%
You will get the tests back sometime this week. I still have students who need to take it!
The scores are on Infinite Campus

4. Learning Objective(s)
By the end of this period you will be able to:
SWBAT prove triangles congruent by using SSS, SAS, ASA, AAS, and HL

5. Exploration Activity
In order to prove that triangles are congruent you need to show that:
All the angles are congruent
All the sides are congruent
However, there are five shortcuts! We will be investigating these with your table-mates.

6. Exploration Activity
With your table, fill out the following worksheet.
You will need
A straightedge
A protractor
If you do not have the following, you will lose participation points.

7. Triangle Congruence Activity
Expectations:
You will work as a table. Everyone must be on the same problem.
You as a team are responsible for keeping one another on task.
I do not want to hear off topic discussions.
You will discuss with your tablemates.
“What did you get for the angle measures?”
“Why are my sides different from yours?”

8. 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:
SSS
SAS
ASA
AAS HL
Right now, we are going to discuss SSS and SAS.

9. 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?
ABC FDE

10. Examples
Non-Examples

11. 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.

12. Whiteboards What is the included angle between the sides BC and CA?
What are the sides of the included angle A?

13. 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?
ABC EFD

14. Example/ Non-Examples

15. 4-4 Triangle Congruence: SSS and SAS
Example 1:
Explain why ∆ABC  ∆DBC.
Use the following sentence frame:
It is given that ____  ____ and __  ______
By the ___________________________, ____ _____. Therefore ________  _________ by ________
It is given that AC  DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

16. 4-4 Triangle Congruence: SSS and SAS
Example 1(b) :
Explain why ∆XYZ  ∆VWZ.
It is given that ____  ____ and __  ______
By the __________________________________________, ____ _____. Therefore ________  _________ by ________

17. Whiteboards Explain why ∆ABC  ∆CDA.
It is given that ____  ____ and __  ______
By the ___________ ____________ of Congruence, ____ _____. Therefore ________  _________ by ________
It is given that AB  CD and BC  DA.
By the Reflexive Property of Congruence, AC  CA.
So ∆ABC  ∆CDA by SSS.

18. 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.

19. 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.

20. Whiteboards ∆STU  ∆VWX, when y = 4. ST  VW, TU  WX, and T  W.
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.

21. 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:
Given: BC || AD, BC  AD

22. 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.

23. Math Joke of the Day
What do you call a broken angle?
A rectangle!

24. Change it to 4.5
On top of your 4.4 Triangle Congruence: ASA< AAS, and HL please change it to 4.5

25. 4.5 Triangle Congruence: SSS and SAS
There are five ways to prove triangles are congruent:
SSS earlier today ( or on Wednesday – per 6)
SAS
ASA Today!
AAS HL

26. Included Side
Earlier, we learned what an included angle is. What do you think an included side would be?

27. Included side
common side of two consecutive angles in a polygon.

28. 4-4 Triangle Congruence: SSS and SAS
Angle–Side–Angle Congruence (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
. What is a possible congruent statement for the figures?
ABC FDE

29. ASA
Examples
Non-Examples

30. Angle-Angle-Side Congruence
Angle-Angle-Side(AAS)
If two angles and a non-included side of one triangle are congruent to the corresponding angles and a side of a second triangle, then the two triangles are congruent.
What is the possible congruence statement for the figures?
ABC EFD

31. Example/ Non-Examples: AAS

32. Example 1 (a) Example 1: Explain why ∆UXV  ∆WXV.
It is given that ____  ____. ________ is a right angle so ______ is also a right angle by ______________.
Therefore, ____________  ____________. (add this sentence frame into your notes)
By the __________________________________________, ____ _____. Therefore ________  _________ by ________
It is given that AC  DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

33. Example 1 (b) Example 1: (b) Explain why ∆ECS  ∆TRS.
This time, I am not going to give you a sentence frame, but I still want you to use COMPLETE SENTENCES to explain why the triangles are congruent.
It is given that AC  DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

34. Determine if you can use ASA to prove NKL  LMN. Explain.
Whiteboard
Determine if you can use ASA to prove
NKL  LMN. Explain. No
By the Alternate Interior Angles Theorem. KLN  MNL. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied.

35. Whiteboard! On your whiteboard, draw a right triangle
Label the legs of the triangle
Label the hypotenuse
It is given that AC  DC and that AB  DB. By the Reflexive Property of Congruence, BC  BC. Therefore ∆ABC  ∆DBC by SSS.

36. Hypotenuse-Leg (HL) Congruence
Hypotenuse-Leg Congruence (HL)
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
IMPORTANT: The hypotenuse is ALWAYS across from the right angle ( highlight this in your notes)
ABC EFD

37. Examples/Non-Examples: HL

38. Identify the postulate or theorem that proves the triangles congruent.
Whiteboards
Identify the postulate or theorem that proves the triangles congruent. HL
ASA
ASA HL
SAS or SSSS
SAS or SSS

39. Example 2

40. Proof Practice!

41. Whiteboard Flash! I am going to show you two triangles
You are going to write down whether they are congruent by SSS, SAS, AAS, ASA, or HL!
Once your entire table thinks they have it correct, STAND UP!
First table to have ALL their members stand up with the correct statement wins that round.
Note: The triangles might not be congruent. If so, state they are not congruent.
ABC EFD

61. Part II: Missing Info
State what additional information is required in order to know that the triangles are congruent for the reason given.