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

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

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

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

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.

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

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-

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.

* 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.

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.

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.

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

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.

Sum it up for us: Conditional statement Converse Inverse Contrapositive

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

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

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

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

Complete each congruence statement. B A ECD C E D

Complete each congruence statement. GTK T G K H

Ex 1 DFE UVW

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

Proving Trianlges Congruent

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

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

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

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

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

Proving Triangles Congruent SSS SAS ASA AAS HL Proving Triangles Congruent

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

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

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

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

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

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

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

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

Congruent Right Triangles HL HYPOTENUSE AND LEG

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 ______

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

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

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

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

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

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

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

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

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