examine each statement. determine whether it is true or false. if false, explain why. 1.if an animal...

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 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:

Try it on your ownTry it on your own

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

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.

Kfed:

• If you give Kfed money, then he makes an awesome album.– Hypothesis-

– Conclusion-

you give K-fed money

he makes and awesome album

• 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.

Try it on your ownTry it on your own

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.

Try it on your ownTry it on your own

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.

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

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.

CA

E

D

B

F

? ABC DEF

Complete each congruence statement.

C

A

ED

B

? ACB ECD

Complete each congruence statement.

KG

H

T ? GHK GTK

Ex 1

statement. congruence a Write.

and , , trianglesIn two

UWDE

VWFEUVDF

DFE UVW

RST is congruent to XYZ. Find the value of n.S

T

R 50° 70°

60°

XY

Z

2n+10°

Since RST is congruent to XYZ, the corresponding parts are congruent.

m S m Y 60 = 2n+10

50 = 2n

n = 25

A

B C F

D

E

AB DF

BC FE

AC DE

A D B F C E

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

DFEABC

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

A B

C

X Z

Y

INCLUDED ANGLEIt’s stuck in between!

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

INCLUDED SIDEIt’s stuck in between!

A B

C

A B

C

Overlapping sides are congruent in

each triangle by the REFLEXIVE property

Vertical Angles

are congruen

t

Alt Int Angles are congruent

given parallel

lines

}The Only Ways To Prove

Triangles Are Congruent

NO BAD WORDS

Side-Side-Side (SSS) Congruence Postulate

66

4 45 5

All Three sides in one triangle are congruent to all three sides

in the other triangle

Are these triangles congruent?

D

O

G

C

A

T

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.

C

A

TH

A

T

Angle-Side-Angle (ASA) Congruence Postulate

Two angles and the INCLUDED side

Are these triangles congruent?

If so, write the congruence statement

B

I

G

T

O

E

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

Are these triangles congruent?

If so, write a congruence statement.

T

O

P H

A

T

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 ______

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

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

Not congruent.Not enough Information to Tell

R

TS

B

A C

Determine if whether the triangles are congruent. If they are, write a congruency statement explaining why they are

congruent.

Ex 3

Determine if whether the triangles are congruent. If they are, write a congruency

statement explaining why they are congruent.

ΔJMK ΔLKM by SAS

J K

LM

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

Determine if whether the triangles are congruent. If they are, write a congruency

statement explaining why they are congruent.

ΔABC ΔEDC by ASA

B A

C

ED

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 SSST

U

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

Homework:

1. Finish Logic Sheet if you didn’t turn it in

2. Pg 255 # 14 – 15 and # 17 – 19