Transcript 4.2 Ways to Prove Triangles Congruent

Geometry
4.2 Ways to Prove Triangles
Congruent
Vocabulary
A
C
7
AB is included between
B
A and
7
7
AB is opposite…
B
C
7
A is opposite… BC
7
A is included between… AB and AC
W
WY is a common side of the two triangles.
X
Y
Z
B
Think about this…
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A
Y
C
X
Z
If two triangles are congruent, then there are
6 parts (angles and sides) of one triangle that are
__
6 corresponding parts of
congruent to the __
the other triangle. 3 angles and 3 sides.
However, it is not necessary to compare all
six parts to show the triangles are congruent.
Triangles may be shown congruent by having
3 pairs of corresponding parts
only __
congruent. The next three postulates cover
this. angles or sides
SSS Postulate
If three sides of one triangle are congruent to three sides of
another triangle, then the triangles are congruent.
S
B
A
R
C
~
ABC =
T
RST by SSS Post.
SAS Postulate
If two sides and the included angle of one triangle are congruent
to two sides and the included angle of another triangle, then the
triangles are congruent.
F
Q
E
P
G
EFG ~
=
R
PQR by SAS Post.
ASA Postulate
If two angles and the included side of one triangle are congruent
to two angles and the included side of another triangle, then the
M
triangles are congruent.
Y
N
Z
L
X
XYZ ~
=
LMN by ASA Post.
~
ABC =
~
TUV =
No Congruence.
ADC by SSS Post.
~
PQS
=
~
EFG =
EHG by ASA Post.
RSQ by SAS Post.
~
ABC =
OPQ by SSS Post.
ZYX by SAS Post.
No Congruence.
WXV by ASA Post.
~
LMN =
HW
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P. 124-126 CE #1-10 WE #1-16
Quiz Thursday
Let’s Try This One!
Given: DC bisects ACB
AC = BC
Prove:
ADC = BDC
7
We will use either the SSS, SAS,
or the ASA Postulate.
Use our proof steps on the board!
A
D
B
C
Let’s Try A Few Together
Are the triangles congruent? If yes, write the
congruence (write the three letters in correct order) and
state the postulate used. If no, say no congruence.
1)
B
C
2)
J
ABC ~
= CDA
A
D
J
A
BAG ~
= JOG
by ASA Post.
G
B
K
N
by SSS Post.
3)
M
O
L
~
No =
Why not?
The angle is not
the included angle
thus this could be
the case…
Let’s try a few from the HW
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Please open your books to page 125
#11 and #15