1. Triangle Inequalities Do now:
Are There Congruence Shortcuts?
Objectives:
Explore shortcut methods for determining whether triangles are congruent
Discover the SSS and SAS are valid congruence shortcuts but SSA is not
Homework: 4.4 pg # 4-9, 12-14, 23, 24
Triangle Inequalities
Do now:

2. Quiz

3. A building contractor has just assembled two massive triangular trusses to support the roof of a recreation hall. Before the crane hoists them into place, the contractor needs to verify that the two triangular trusses are identical. Must the contractor measure and compare all six parts of both triangles?
Wikipedia: In architecture a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes.

5.
for SSA:

6. Explain what the picture statement means.
Create a picture statement to represent the SAS Triangle Congruence Conjecture.
Explain what the picture statement means.
In the third investigation you discovered that the SSA case is not a triangle congruence shortcut. Sketch a counterexample to show why.

7. Which conjecture tells you that triangles are congruent?
Closing the Lesson: The main points of this lesson are that SSS and SAS can be used to establish the congruence of triangles but SSA cannot.
What is the reason why SSA fails?
Y is a midpoint

8. 4.4-4.5 Are There Congruence Shortcuts? Objectives:
Explore shortcut methods for determining whether triangles are congruent
Discover valid congruence shortcuts
Homework: 4.5 pg.229 # 4, 6, 8, 10, 12, 14
Do Now:
# 4-6,10(!) pg. 224

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

10. Side-Side-Side (SSS)
AB  DE
BC  EF
AC  DF
ABC   DEF B A C E D F

11. Side-Angle-Side (SAS)B E F A C D
AB  DE
A   D
AC  DF
ABC   DEF
included
angle

12. Included Angle
The angle between two sides
 H
 G
 I

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

14. Angle-Side-Angle (ASA)B E F A C D
A   D
AB  DE
 B   E
ABC   DEF
included
side

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. Angle-Angle-Side (AAS)B E F A C D
A   D
 B   E
BC  EF
ABC   DEF
Non-included
side

18. There is no such thing as an SSA conjecture!
Warning: No SSA Conjecture
There is no such thing as an SSA conjecture! E B F A C D
NOT CONGRUENT

19. There is no such thing as an AAA conjecture!
Warning: No AAA Conjecture
There is no such thing as an AAA conjecture! E B A C F D
NOT CONGRUENT

20. The Congruence Conjectures
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
SSA correspondence
AAA correspondence

21. Name That Conjecture
(when possible)
SAS
ASA
SSA
SSS

22. Name That Conjecture
(when possible)
AAA
ASA
SSA
SAS

23. Name That Conjecture SAS SAS SSA SAS Vertical Angles
(when possible)
Vertical Angles
Reflexive Property
SAS
SAS
Vertical Angles
Reflexive Property
SSA
SAS

24. 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:

25. Name That Conjecture
(when possible)

26. 10. The perimeter of ABC is 180 m.
Is ABC ADE? Which conjecture supports your conclusion?

27. Name That Conjecture
(when possible)

28. Indicate the additional information needed to enable us to apply the specified congruence postulate.
For ASA:
For SAS:
For AAS:

29. Determine whether the triangles are congruent, and name the congruence shortcut. If the triangles cannot be shown to be congruent, write
“cannot be determined.”

30. Solve: pg # 11-19
pg.229 # 6-9
Pg.230 # 13, 15, 18
Shortcut for showing triangle congruence allows us to avoid proving the congruence of all six pairs of corresponding parts. There are four shortcuts for proving triangle congruence. Students discovered SSS and SAS in the previous lesson. Now they have discovered ASA and SAA. SSA and AAA are not congruence shortcuts. Other arrangements of the letters, such as ASS (not a shortcut) and AAS (a shortcut), are included among these six.

31. CPCTC-Corresponding Parts of Congruent Triangles are Congruent
Objectives:
Show that pairs of angles or pairs of sides are congruent by identifying related triangles
Homework: lesson 4.6 pg.233 # 3, 4, 5, pg. 231 # 26
Do now:
CPCTC-Corresponding Parts of Congruent
Triangles are Congruent

33. Paragraph proof

34. Together: # 1, 2 pg 233 # 12

35. CPCTC-Corresponding Parts of Congruent Triangles are Congruent
Objectives:
Show that pairs of angles or pairs of sides are congruent by identifying related triangles
Homework: lesson 4.6 pg # 6, 7, 9, 18
Do now:
CPCTC-Corresponding Parts of Congruent
Triangles are Congruent

36. In Chapter 3, you used inductive reasoning to discover how to duplicate an angle using a compass and straightedge. Now you have the skills to explain why the construction works using deductive reasoning. The construction is shown at right.Write a paragraph proof explaining why it works.
Practice:

37. # 3 (from h/w)

38. # 3 (from h/w)

39. #5 (h/w)

40. #6

43. Closure: To show that two segments or angles (the targets) are congruent, you will often find two congruent triangles in which these segments or angles are corresponding parts.