Transcript 1 Congruence Postulates

ACC Math 1
EQ:
What does it mean for two triangles
to be congruent?
Congruent figures have the same size
and same shape.
The parts of congruent triangles that
“match” are called corresponding parts.
Two polygons are congruent if ALL pairs
of corresponding parts are congruent.
In a congruence statement
ORDER MATTERS!!!!
Everything matches up.
NOV  DAY
Complete each congruence statement.
B
A
D
C
F
ABC   DEF
?
E
Complete each congruence statement.
B
A
ACB   ECD
?
C
D
E
Complete each congruence statement.
G
T
GHK   GTK
?
K
H
Fill in the blanks
EGF
BCA   ____
CAB   GFE
____
Complete the congruence statement.
MKL   JKN
_____
Complete the congruence statement.
ABD   CBD
_____
Corresponding Parts of
Congruent Triangles are
Congruent
Fill in the blanks
O
If CAT  DOG, then A  ___
CPCTC
because ________.
O
C
D
G
A
T
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
_______.
Complete each congruence statement.
If ABC  DEF,
then BC  EF
___
Fill in the blanks
If CAT  DOG,
thenA
___  O.
Fill in the blanks
BAT  MON
T  N
___
ATB
_____  ONM
BA  MO
_____
NM  TB
____
There are 5 ways
to prove triangles
congruent.
Side-Side-Side (SSS) Congruence
Postulate
All 3 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
(the angle is in between the 2
marked sides)
Angle-Side-Angle (ASA)
Congruence Postulate
Two angles and the INCLUDED side
(the side is in between the 2 marked angles)
Angle-Angle-Side (AAS)
Congruence Postulate
Two Angles and One Side
that is NOT included
There is one more way to prove
triangles congruent, but it’s only for
RIGHT TRIANGLES
}
NO BAD
WORDS
Your Only Ways
To Prove
Triangles Are
Congruent
There are only 3 types
of markings YOU can
add to a triangle if
they are not already
marked.
Overlapping sides are
congruent in each
triangle by the
REFLEXIVE property
Alt Int
Angles are
Vertical
Angles are congruent
given
congruent
parallel lines
Ex 1
SSS, SAS, ASA, AAS, HL, or not congruent.
SSS
SSS, SAS, ASA, AAS, HL, or not congruent.
Ex 2
I
AAS
Ex 3
SSS, SAS, ASA, AAS, HL, or not congruent.
Not congruent.
Ex 4
SSS, SAS, ASA, AAS, HL, or not congruent.
SAS
SSS, SAS, ASA, AAS, HL, or not congruent.
Ex 5
ASA
Ex 6
SSS, SAS, ASA, AAS, HL, or not congruent.
SSS
SSS, SAS, ASA, AAS, HL, or not congruent.
Ex 7
Not congruent
SSS, SAS, ASA, AAS, HL, or not congruent.
Ex 8
SAS
Ex 9
SSS, SAS, ASA, AAS, HL, or not congruent.
Not congruent.
Ex 10
SSS, SAS, ASA, AAS, HL, or not congruent.
HL
Ex 11
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 12
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