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**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

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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 out the problem independently & then share your work with your partner Work together from the get-go

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**Objective: Recognize and analyze a conditional statements**

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. Truth Values?

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**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-

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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! 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.

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

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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.**

B DEF A C D F E

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**Complete each congruence statement.**

B A ECD C E D

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**Complete each congruence statement.**

GTK T G K H

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Ex 1 DFE UVW

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**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

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Proving Trianlges Congruent

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**TO PROVE TRIANGLES ARE CONGRUENT YOU DO NOT NEED TO KNOW ALL SIX**

B C E F 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**

C X Z Y INCLUDED ANGLE It’s stuck in between!

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**Before we start…let’s get a few things straight**

C A B C INCLUDED SIDE It’s stuck in between!

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**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

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**The Only Ways To Prove Triangles Are Congruent**

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

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**Proving Triangles Congruent**

SSS SAS ASA AAS HL Proving Triangles Congruent

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**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

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**Are these triangles congruent?**

D G A 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.

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**Angle-Side-Angle (ASA) Congruence Postulate**

Two angles and the INCLUDED side

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**Are these triangles congruent?**

B G O If so, write the congruence statement

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**Angle-Angle-Side (AAS) Congruence Postulate**

Two Angles and One Side that is NOT included

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**If so, write a congruence statement.**

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

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**Congruent Right Triangles**

HL HYPOTENUSE AND LEG

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**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 ______

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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4.6 Prove Triangles Congruent by ASA and AAS

4.6 Prove Triangles Congruent by ASA and AAS

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