Download Triangle Congruence Powerpoint

Session 6
Daily Check
1) UW and VW 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)
Homework Review
Essential Question: What does it mean for two triangles
to be congruent and what does CPCTC mean?
CCGPS Analytic Geometry
Day 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
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.
B
A
D
C
F
ABC   DEF
?
E
Essential Question: What does it mean for two triangles
to be congruent and what does CPCTC mean?
A
Complete each congruence
statement.
B
ACB   ECD
?
C
D
E
Essential Question: What does it mean for two triangles
to be congruent and what does CPCTC mean?
Complete each congruence
statement.
T
GHK   GTK
?
G
K
H
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
O
If CAT  DOG, then A  ___
CPCTC
because ________.
O
C
D
G
A
T
Essential Question: What does it mean for two triangles
to be congruent and what does CPCTC mean?
Fill in the blanks
RS
If FJH  QRS, then JH  ___
Q because _______.
CPCTC
and F  ___
If XYZ  ABC, then ZX  CA
___
and Y  B
___ because CPCTC
_______.
Essential Question: What does it mean for two triangles
to be congruent and what does CPCTC mean?
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
congruent
Alt Int
Angles are
congruent
given
parallel lines
Before we start…let’s get a few things straight
C
A
Y
B
X
INCLUDED ANGLE
Z
Side-Side-Side (SSS) Congruence
Postulate
4
5
6
4
5
6
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
In two triangles , DF  UV , FE  VW and
DE  UW . Write a congruence statement.
 DFE   UVW
SSS
by ____
Ex 2
Determine whether the triangles are congruent. If they are, write
a congruency statement explaining why they are congruent.
R
S
T
ΔRST  ΔYZX by SSS
Ex 3
Determine whether the triangles are congruent. If they are, write
a congruency statement explaining why they are congruent.
R
T
S
Not congruent.
Not enough Information to Tell
Ex 4
Determine whether the triangles are congruent. If they are, write
a congruency statement explaining why they are congruent.
P
R
S
Q
ΔPQS  ΔPRS by SAS
Ex 5
Determine whether the triangles are congruent. If they are, write
a congruency statement explaining why they are congruent.
P
S
Q
U
R
T
ΔPQR  ΔSTU by SSS
Ex 6
Determine whether the triangles are congruent. If they are, write
a congruency statement explaining why they are congruent.
M
P
R
N
Q
Not congruent.
Not enough Information to Tell
Before we start…let’s get a few things straight
C
A
Y
B
X
INCLUDED SIDE
Z
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
}
NO BAD
WORDS
Your Only Ways
To Prove
Triangles Are
Congruent
Ex 1
In ΔDEF and ΔLMN , D  N , DE  NL and
E  L. Write a congruence statement.
 DEF   NLM
ASA
by ____
Ex 2
What other pair of angles needs to be marked so
that the two triangles are congruent by AAS?
D
E  N
L
M
F
E
N
Ex 3
What other pair of angles needs to be marked so
that the two triangles are congruent by ASA?
D
D  L
L
M
F
E
N
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.
Ex 4
G
K
I
H
J
ΔGIH  ΔJIK by AAS
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.
Ex 5
B
A
C
D
E
ΔABC  ΔEDC by ASA
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.
Ex 6
E
A
C
B
D
ΔACB  ΔECD by SAS
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.
Ex 7
J
T
K
L
V
Not possible
U