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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 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:
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
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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.
Try it on your ownTry it on your own
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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.
Try it on your ownTry it on your own
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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
? ABC DEF
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Complete each congruence statement.
C
A
ED
B
? ACB ECD
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Complete each congruence statement.
KG
H
T ? GHK GTK
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Ex 1
statement. congruence a Write.
and , , trianglesIn two
UWDE
VWFEUVDF
DFE UVW
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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
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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
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Before we start…let’s get a few things straight
A B
C
X Z
Y
INCLUDED ANGLEIt’s stuck in between!
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Before we start…let’s get a few things straight
INCLUDED SIDEIt’s stuck in between!
A B
C
A B
C
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Overlapping sides are congruent in
each triangle by the REFLEXIVE property
Vertical Angles
are congruen
t
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 45 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
TH
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
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
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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
J K
LM
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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
B A
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 SSST
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