1. Congruent Triangle Shortcuts
DO NOW 11/17:
How can you create two congruent triangles from the kite below? Use the properties of a kite to explain your answer.
Congruent Triangle Shortcuts
Agenda
Congruence and Rigid Motion
Corresponding Parts and Tips
SSS and SAS
Exit Ticket/Debrief

2. Congruence and Polygons
Two figures are congruent if they have exactly the same size and shape.
Two polygons are congruent if they have congruent corresponding sides and angles
Specifically,  triangles have 3  corresponding sides and 3  corresponding <s A C B D E F
*MUST BE IN NOTES!*

3. Rigid Motions and Congruence
Since rigid transformations move every point the same way, the resulting figure remains congruent.
Translations, rotations and reflections all result in congruent images.
Therefore, if we can transform a figure to land on top of itself, we can identify the parts of that figure that are corresponding and congruent. B A C B A C

4. Corresponding Parts
If all 6 pairs of corresponding parts (sides and angles) are , then the triangles are . B A C
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF E D F

5. Steps and Tricks a) Reflexive Sides b) Vertical Angles
1. Mark everything that is given
2. BEWARE OF and MARK:
a) Reflexive Sides
(remember Reflexive Property of Congruence: AB  AB)
b) Vertical Angles
(across from each other and  )
3. Look for short-cuts that match the theorems
*MUST BE IN NOTES!*

6. Do you need all 6 ?
NO !
SSS
SAS
ASA
AAS

7. Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF
SSS: If 3 sides of 1 triangle are  to 3 sides of another triangle, then the 2 triangles are .
*MUST BE IN NOTES!*

8. Side-Angle-Side (SAS)B F A D C
AB  DE
A   D
AC  DF
ABC   DEF
included
angle
SAS: If 2 sides of 1 triangle are  to 2 sides of another triangle and the included < of 1 triangle is  to the included < of another triangle, then the 2 triangles are .
*MUST BE IN NOTES!*

9. Included Angle
Is the < between or INside 2 sides
 H
 G
 I

10. Included Angle Name the included angle: YE and ES ES and YS YS and YE

11. Name That Postulate
(when possible)
SAS
SAS
ASS
SSS

12. Name That Postulate SAS SAS ASS SAS Vertical Angles Reflexive Property
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
Vertical Angles
Reflexive Property
ASS
SAS

13. Triangle Congruence Shortcuts #2
DO NOW 11/18:
Triangle Congruence Shortcuts #2
Agenda
HW Review
ASA and AAS
Algebra Practice
Debreif/Exit

14. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
Included side
ASA: If 2 <s of 1 triangle are  to 2 <s of another triangle and the included side of 1 triangle is  to the included side of another triangle, then the 2 triangles are .

15. Included Side
The side between two angles GI GH HI

16. Included Side Name the included side: Y and E E and S S and Y YEES SY

17. Example
From the information in the diagram, can you prove that ΔFDG and ΔFDE are congruent? Explain.
yes; AAA
yes; ASA
yes; SSS no

18. Angle-Angle-Side (AAS)B E F A C D
A   D
 B   E
BC  EF
ABC   DEF
Non-included
side
AAS: If 2 <s of 1 triangle are  to 2 <s of another triangle and the non-included side of 1 triangle is  to the non-included side of another triangle, then the 2 triangles are .

19. There is no such thing as an ASS postulate!
Warning: No ASS Postulate
There is no such thing as an ASS postulate!
NOT CONGRUENT

20. There is no such thing as an AAA postulate!
Warning: No AAA Postulate
There is no such thing as an AAA postulate! E B C A F D
NOT CONGRUENT

21. The Congruence Postulates
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
ASS correspondence
AAA correspondence

22. Name That Postulate
(when possible)
SAS
ASA
ASS
SSS

23. Name That Postulate
(when possible)
AAA
ASA
ASS
SAS

24. Determine which triangles are congruent by AAS using the information in the diagram below.
ΔABE ≅ ΔCBE
ΔABF ≅ ΔEDF
ΔABE ≅ ΔEDA
ΔADC ≅ ΔEBC
Name the postulate that proves that the triangles are congruent. (Hint: What type of triangle is this and what are its special properties?)
SAS
AAS
ASA
ASS

25. Let’s Practice B  D AC  FE A  F
Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
B  D
For SAS:
AC  FE
A  F
For AAS:

26. Transformations and Congruence
DO NOW 11/19:
Identify if the two triangles are congruent using a congruence shortcut. Then solve for x.
(3x+5) cm
26 cm
Transformations and Congruence
Agenda
Note Check/HW
CPCTC
GeoGebra Investigation
Exit Ticket/Debrief

27. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Once we use congruence shortcuts to identify that two triangles are congruent, we know that ALL corresponding parts of those triangles are congruent.

28. Debrief: Transformations and Proving Triangle Congruence
How can we use transformations to show that our triangle congruence shortcuts work?
How would we use a formal two column proof to show that two triangles are congruent?

29. Flow Chart Proof DO NOW 11/20:
Label the diagram with the given information. What congruence shortcut can we use to prove that AB and DC are parallel?
Flow Chart Proof
Agenda
Congruence Shortcuts Quiz
Flow Chart Proof
Flow Chart Example
Debrief

30. Flow Chart Proofs
Like a two column proof, flow chart proofs start with given information and use logic to arrive at a conclusion (“prove”)
Flow charts contain statements (boxes) that must be supported by reasons (lines underneath boxes)

31. Flow Chart Proof (Do Now)

32. Flow Chart Proof (Independent Practice)

33. Debrief
What are some advantages/disadvantages to flow chart proof over two-column proofs?