Download DOES SSS ESTABLISH TRIANGLE CONGRUENCE? YES!!! DOES

G.CO,8 STUDENT NOTES & PRACTICE WS #7
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geometrycommoncore.com
DOES SSS ESTABLISH TRIANGLE CONGRUENCE? YES!!!
AABC = AWER (SSS)
k.fr.
"P"
AABD
=
ACBD (SSSI
ATHJ = ARJH
DOES SAS ESTABLISH TRIANGLE-CONGRUENCE? YES!!!
AGHK = AGFK (SAS) or (SSS)
AABC = AUYM (SAS)
AABC = AHBM (SAS)
DOES ASA ESTABLISH TRIANGLE CONGRUENCE? YES!!!
ABTG
=
AETG {AsA)
AGTE
=
AGYD (AsA)
ATEG
=
AULK {ASA)
DOES AAS/SAA ESTABLISH TRIANGTE CONGRUENCE? YES!!!
this is a special form of ASA. In any triangle, if you have two angles you are able to determine the third
angle because they sum to 180o. So by knowing two angles, you actually know three angles. So ASA and
AAS/SAA both work as congruence relationships.
Yes,
ANGLE-SIDE-ANGLE
Third Angles are Congruent.
ANGLE-ANGTE.SIDE
G.CO.8 STUDENT NOTES & PRACTICE WS #7
-
geometrycommoncore.com
2
RUENCE? SOMETIMES.....
This is a difficult case.... it sometimes produces congruence and other times it doesn't. We will look at each
case
to see when it works and when it doesn't.
CASE
#L-
AS1S2,
when
Sz is
greater than Sr.
This forms a triangle congruence relationship. There is only one way for
be placed to complete the triangle.
CASE #2
-
ASrSz,
when
Sz
Sz
to
is less than 51. (Too Short)
This is a weird case but when establishing all things that could happen we need
to include this. lt is possible that Sz is not long enough to close the triangle.
This of course is not a congruence relationship, it doesn't even form a triangle.
CASE #3
-
ASrSz,
when
Sz is less
than Sr (1 lntersection)
-
This case is typically known as HL, which stands for Hypotenuse
Leg. tt gets this special name because it is the right triangle that locks this
shape. A way to understand why this forms a congruence relationship is
because in a right triangle if you know two sides, you can use the Pythagorean
Theorem to calculate the third side. Now you have SSS or SAS, which we have
already established to be congruence criteria. HL forms a triangle congruence
relationship.
CASE #4
-
ASrSz,
when
Sz
,t' I,
,t' I,
is less than Sr. (2 lntersections)
This is known as the AMBIGIOUS CASE because two different triangles can be
formed by this information. Because 52 is shorter it can swing to form two
possiblelocations.ThisdoesNoTformatrianglecongruencerelationship.il,,
N}"IIS
(Now You Trv Somel
1. Are the following pairs of triangles congruent?
<1
€v
lf they arg.then name their congruence criteria. (SSS, SAS, ASA, AAS, HL or AS1S2 (Sz > Sr))
a)yes6r-
o)@/*o
5AS-
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SSS-
ar@ruo
tA(S
geometrycommoncore.com
G'co.8 sruDENT NoTEs & pRAcrtcE ws #r
z
2' Are the following pairs of triangle congruent? yEs,
lf
create a congruence statement and name
the
congruence criteria (SS$ SAS, ASA, AAS,
HL or AS1S2 (Sz >
Sr)).
@z*o
a)
A-EDC _=A_HNC
criteria AIS/S
@/
b)
A_C
t*
ruo
eD = A_CE R
ftSA
criteria
cED =A_E!T
^
s.A6
Criteria
d)
@z
*o
A_lr-Dc_ = [ KLP{
Criteria A
e)
Criteria
ves
l
Se
(1-o\
Sz)Sr
.k"