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
Apr 01, 2015
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