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Examine each statement. Determine whether it is true or false. If false, explain why.

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 x 2 = 9. Foundations: basic logic, writing skills .

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Examine each statement. Determine whether it is true or false. If false, explain why.

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  1. 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. 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. you give K-fed money • he makes and awesome album Kfed: • 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 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. S Z 60° R 50° 70° T Y 2n+10° X RST is congruent to XYZ. Find the value of n. Since  RST is congruent to XYZ, the corresponding parts are congruent. 60 = 2n+10 50 = 2n n = 25

  23. Proving Trianlges Congruent

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

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

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

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

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

  29. SSS SAS ASA AAS HL Proving Triangles Congruent

  30. Side-Side-Side (SSS) Congruence Postulate 4 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? O T C 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? A A T T C H If so, write the congruence statement.

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

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

  38. Congruent Right Triangles HL HYPOTENUSE AND LEG

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

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

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

  43. 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. Ex 4 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. B A C D E Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. ΔABC ΔEDC by ASA

  46. Ex 5 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. 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. Homework: Finish Logic Sheet if you didn’t turn it in Pg 255 # 14 – 15 and # 17 – 19

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