Presentation is loading. Please wait.

Presentation is loading. Please wait.

Examine each statement. Determine whether it is true or false. If false, explain why. 1.If an animal is a bird, then it is a penguin. 2.If it rains, then.

Similar presentations


Presentation on theme: "Examine each statement. Determine whether it is true or false. If false, explain why. 1.If an animal is a bird, then it is a penguin. 2.If it rains, then."— Presentation transcript:

1

2 Examine each statement. Determine whether it is true or false. If false, explain why. 1.If an animal is a bird, then it is a penguin. 2.If it rains, then the football game will be cancelled. 3.If x > 2, then x > 5. 4.If x = 3, then x 2 = 9

3 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

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

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

6 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.

7 Hypothesis and Conclusion If it is sunny outside, then it is hot.

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

9 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.

10 * 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.

11 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.

12 NO HOMEWORK FOR A MONTH! 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.

13 When you negate the hypothesis and conclusion of the converse of a conditional statement, you form the contrapositive.

14 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.

15 Sum it up for us: Conditional statement Converse Inverse Contrapositive

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

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

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

19 Complete each congruence statement. CA E D B F DEF

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

21 Complete each congruence statement. K G H T GTK

22 Ex 1 DFEUVW

23  RST is congruent to  XYZ. Find the value of n. S T R 50° 70° 60° X Y Z 2n+10° Since  RST is congruent to  XYZ, the corresponding parts are congruent. 60 = 2n+10 50 = 2n n = 25

24

25 A BCF D E TO PROVE TRIANGLES ARE CONGRUENT YOU DO NOT NEED TO KNOW ALL SIX

26 Before we start…let’s get a few things straight AB C XZ Y INCLUDED ANGLE It’s stuck in between!

27 Before we start…let’s get a few things straight INCLUDED SIDE It’s stuck in between! AB C AB C

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

29 The Only Ways To Prove Triangles Are Congruent NO BAD WORDS

30

31 Side-Side-Side (SSS) Congruence Postulate 66 4 4 5 5 All Three sides in one triangle are congruent to all three sides in the other triangle

32 Are these triangles congruent? D O G C A T If so, write the congruence statement.

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

34 Are these triangles congruent? If so, write the congruence statement. C A T H A T

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

36 Are these triangles congruent? If so, write the congruence statement B I G T O E

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

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

39

40 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 ______

41 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 Ex 2

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

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

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

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

46 Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. ΔABC  ΔEDC by ASA BA C ED

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

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

49 Homework: 1.Finish Logic Sheet if you didn’t turn it in 2.Pg 255 # 14 – 15 and # 17 – 19


Download ppt "Examine each statement. Determine whether it is true or false. If false, explain why. 1.If an animal is a bird, then it is a penguin. 2.If it rains, then."

Similar presentations


Ads by Google