Post on 05-Jan-2016
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Session 6 Daily Check1) and are midsegments of the triangle. Find the length of RT and UW. (2 points each)
2) Use the Triangle Proportionality Theorem to solve for x. (3 points each) a) b)
UW VW
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Homework Review
CCGPS Analytic GeometryDay 6 (8-21-13)
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
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.
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
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.
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.
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Corresponding Parts of Congruent Triangles are
Congruent
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
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
Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?
Overlapping sides are congruent in
each triangle by the REFLEXIVE property
Vertical Angles
are congruen
t
Alt Int Angles are congruent
given parallel
lines
Before we start…let’s get a few things straight
A B
C
X Z
Y
INCLUDED ANGLE
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
Side-Angle-Side (SAS) Congruence Postulate
Two sides and the INCLUDED angle
Ex 1
statement. congruence a Write.
and , , trianglesIn two
UWDE
VWFEUVDF
DFE UVW
by ____SSS
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 2
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
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
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
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
Before we start…let’s get a few things straight
INCLUDED SIDE
A B
C
X Z
Y
Angle-Side-Angle (ASA) Congruence Postulate
Two angles and the INCLUDED side
Angle-Angle-Side (AAS) Congruence Postulate
Two Angles and One Side that is NOT included
} Your Only Ways To Prove Triangles Are
Congruent
NO BAD WORDS
Ex 1
statement. congruence a Write.
and ,, and In
LE
NLDENDΔLMNΔDEF
DEF NLM
by ____ASA
Ex 2
What other pair of angles needs to be marked so that the two triangles are congruent by AAS?
F
D
E
M
L
N
NE
Ex 3
What other pair of angles needs to be marked so that the two triangles are congruent by ASA?
F
D
E
M
L
N
LD
Determine whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
ΔGIH ΔJIK by AAS
G
I
H J
KEx 4
ΔABC ΔEDC by ASA
B A
C
ED
Ex 5
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
ΔACB ΔECD by SASB
A
C
E
D
Ex 6
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
Not possible
K
J
L
T
U
Ex 7
Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.
V