1. Examine each statement. Determine whether it is true or false
Examine each statement. Determine whether it is true or false. If false, explain why.
If an animal is a bird, then it is a penguin.
If it rains, then the football game will be cancelled.
If x > 2, then x > 5.
If x = 3, then x2 = 9

2. Foundations: basic logic, writing skills
Essential Question: What are the elements of a conditional statement? What is a converse? What does conditional mean?
Homework: finish logic sheet

3. Keep a Lookout:
Work out the problem independently as we will take a class poll for the answer
Work out the problem independently & then share your work with your partner
Work together from the get-go

4. Objective: Recognize and analyze a conditional statements
Learning Goal #6: LOGIC
Objective: Recognize and analyze a conditional statements

5. Conditional Statements
Called “if-then statements.”
Hypothesis- The part following if.
Conclusion- The part following then.
* Do not include if and then in the hypothesis and conclusion.

6. Hypothesis and Conclusion
If it is sunny outside, then it is hot.
Truth Values?

7. Kfed: you give K-fed money Hypothesis- he makes and awesome album
If you give Kfed money, then he makes an awesome album.
Hypothesis-
Conclusion-

8. The converse of a conditional statement is formed by exchanging the hypothesis and the conclusion.
Conditional- If it is sunny outside, then it is hot.
Converse- If it is hot, then it is sunny outside.

9. * TRUTH VALUE?
Conditional- If a figure is a square, then it has four sides.
Converse- If a figure has four sides, then it is a square.
* Not all four sided figures are squares. Counterexample: Rectangles also have four sides.

10. Rewrite the statement as a conditional statement, then find the converse.
All teenagers are lazy.
Conditional-
Converse-
If you are a teen, then you are lazy.
If you are lazy, then you are a teen.

11. NO HOMEWORK FOR A MONTH! NOT!
When you negate (“not”) the hypothesis and the conclusion of a conditional statement, you form the inverse.
Example:
Cond. Stmt: If is sunny outside, then it is hot.
Inverse: If it is NOT sunny outside, then it is NOT hot.

12. When you negate the hypothesis and conclusion of the converse of a conditional statement, you form the contrapositive.
NOT!

13. Example:
Cond. Stmt: If it is sunny outside, then it is hot.
Converse: If it is hot, then it is sunny outside.
Contrapositive:If it is NOT hot, then it is NOT sunny.

14. Sum it up for us: Conditional statement Converse Inverse
Contrapositive

15. Practice:
Conditional Statements Worksheet
If you don’t finish in class, you must finish and turn in Friday

16. Learning Goal #7: PROOFS
Objective: Understand and Use congruence postulates and theorems for triangles

17. Congruent triangles have congruent sides and congruent angles.
The parts of congruent triangles that “match” are called corresponding parts.

18. Complete each congruence statement.B
DEF A C D F E

19. Complete each congruence statement.B A
ECD C E D

20. Complete each congruence statement.
GTK T G K H

21. Ex 1
DFE
UVW

22. RST is congruent to XYZ. Find the value of n.
50°
70°
60°
Since  RST is congruent to XYZ, the corresponding parts are congruent.
60 = 2n+10
50 = 2n
n = 25

23. Proving Trianlges
Congruent

24. TO PROVE TRIANGLES ARE CONGRUENT YOU DO NOT NEED TO KNOW ALL SIXB C E F
TO PROVE TRIANGLES ARE CONGRUENT YOU DO NOT NEED TO KNOW ALL SIX

25. Before we start…let’s get a few things straightC X Z Y
INCLUDED ANGLE
It’s stuck in between!

26. Before we start…let’s get a few things straightC A B C
INCLUDED SIDE
It’s stuck in between!

27. Alt Int Angles are congruent given parallel lines
Overlapping sides are congruent in each triangle by the REFLEXIVE property
Alt Int Angles are congruent given parallel lines
Vertical Angles are congruent

28. The Only Ways To Prove Triangles Are Congruent
SSS
SAS
ASA
AAS HL
The Only Ways To Prove Triangles Are Congruent
NO BAD WORDS

29. Proving Triangles Congruent
SSS
SAS
ASA
AAS HL
Proving Triangles Congruent

30. Side-Side-Side (SSS) Congruence Postulate4 4 5 5 6 6
All Three sides in one triangle are congruent to all three sides in the other triangle

31. Are these triangles congruent?D G A
If so, write the congruence statement.

32. Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle

33. Are these triangles congruent?
If so, write the congruence statement.

34. Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side

35. Are these triangles congruent?B G O
If so, write the congruence statement

36. Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included

37. If so, write a congruence statement.
Are these triangles congruent? P H A O T T
If so, write a congruence statement.

38. Congruent Right TrianglesHL
HYPOTENUSE AND LEG

39. Δ_____  Δ_____ by ______
The following slides will have pictures of triangles. You are to determine if the triangles are congruent. If they are congruent, then you should write a congruence statement and state which postulate you used to determine congruency.
Δ_____  Δ_____ by ______

40. Ex 2
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S Y X Z
ΔRST  ΔYZX by SSS

41. Determine if whether the triangles are congruent
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. G I H J K
ΔGIH  ΔJIK by AAS

42. Not enough Information to Tell
Ex 3
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S B A C
Not congruent.
Not enough Information to Tell

43. Determine if whether the triangles are congruent
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. J K L M
ΔJMK  ΔLKM by SAS

44. ΔPQS  ΔPRS by SAS Ex 4 P R Q S
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R Q S
ΔPQS  ΔPRS by SAS

45. Determine if whether the triangles are congruent
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. B A C E D
ΔABC  ΔEDC by ASA

46. ΔPQR  ΔSTU by SSS Ex 5 P S U Q R T
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S U Q R T
ΔPQR  ΔSTU by SSS

47. Not enough Information to Tell
Ex 6
Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R Q N
Not congruent.
Not enough Information to Tell

48. Finish Logic Sheet if you didn’t turn it in
Homework:
Finish Logic Sheet if you didn’t turn it in
Pg 255 # 14 – 15 and # 17 – 19