Download - CCGPS Analytic Geometry (8-19-13)
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CCGPS Analytic Geometry(8-19-13)
UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms?Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13
Today’s Question:What does it mean for two triangles to be congruent?Standard: MCC9-12.G.SRT5, CO.7-8
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Congruent triangles have congruent sides and congruent angles.
The parts of congruent triangles that “match” are called corresponding parts.
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Complete each congruence statement.
CA
E
D
B
F
? ABC DEF
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
? ACB ECD
C
A
ED
B
Complete each congruence statement.
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
? GHK GTK
KG
H
T
Complete each congruence statement.
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Corresponding Parts of Congruent Triangles are
Congruent
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Fill in the blanks
If CAT DOG, then A ___
because ________.
O
CPCTCC
A T
O
D
G
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Fill in the blanks
If FJH QRS, then ___ and F ___ because _______.Q CPCTC
J H RS
B CPCTCIf XYZ ABC, then ___ and Y ___ because _______.
ZX CA
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Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
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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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Before we start…let’s get a few things straight
A B
C
X Z
Y
INCLUDED ANGLE
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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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Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle
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Determine 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 1
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Ex 2
statement. congruence a Write.
and , , trianglesIn two
UWDE
VWFEUVDF
DFE UVW
by ____SSS
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Not congruent.Not enough Information to Tell
R
TS
B
A C
Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent.
Ex 3
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Determine 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 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 SSS
T
U
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Determine 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