there are five ways to prove that triangles are congruent. they are: sss, sas, asa, aas, hl
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There are five ways to prove that triangles are congruent. They are: SSS, SAS, ASA, AAS, HL We are going to look at the first three today. SSS Postulate – If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. - PowerPoint PPT PresentationTRANSCRIPT
There are five ways to prove that triangles are congruent. They are:
SSS, SAS, ASA, AAS, HL
We are going to look at the first three today.
SSS Postulate – If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
S – Side S – Side S - SideB
A C F
D
E
ABC FDEbecause of SSS
S: AB FDS: BC DES: AC FE
What SSS Looks Like…
A
B
C
SP Q
R
E
D
F
ABC DEF
PRQ SRQ
S: AB EDS: BC EFS: AC FD
S: PR SRS: PQ SQS: RQ RQ
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.
S – Side A – Angle S - SideB
A C F
D
E
CAB EFD
because of SAS
S: AB FDA: B DS: BC DE
S: WT YZA: W ZS: WV ZX
L M
N
QP
WV
X
T
Y
Z
LMN QPN
YZX TWV
What SAS Looks Like…
S: MN PNA: LNM QNP
S: LN QN
What SAS Does NOT Look Like…
W VX
TY
Z
The angle pair that is marked congruent MUST be in between the two congruent sides to use SAS! There is NOT enough information to determine whether these triangles are congruent.
A: B DS: AB FDA: A F
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 triangles are congruent.
A – Angle S – Side A - Angle
B
A C F
D
E
ACB FED
because of ASA
What ASA Looks Like…
FDG JHG
MNL PRQ
D
G J
H
F
M N
PR
Q
L
A: D HS: DG HGA: DGF HGJ
A: N RS: MN PRA: M P
What ASA Does NOT Look Like…
The pair of sides pair that are marked congruent MUST be in between the two congruent angles to use ASA!
M N P R
QL