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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

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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

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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

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

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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.

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

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

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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.

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* 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.

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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.

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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.

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

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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.

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Sum it up for us: Conditional statement Converse Inverse Contrapositive

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

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

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

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Complete each congruence statement. CA E D B F DEF

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Complete each congruence statement. C A E D B ECD

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Complete each congruence statement. K G H T GTK

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Ex 1 DFEUVW

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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

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

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

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

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

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The Only Ways To Prove Triangles Are Congruent NO BAD WORDS

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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

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

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

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

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

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

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

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

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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 ______

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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

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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

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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

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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

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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

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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

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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

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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

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

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