Name _________________
Date _________
Period ______
Notes 4-5: Triangle Congruence: SSS and SAS
How do you know for sure that two triangles are congruent?
Side-Side-Side (SSS) Congruence Postulate
If _____________of one triangle are congruent to _____________of another triangle,
then the triangles are _____________________.
QR  TU, RP  US,
and
PQ  ST ,
so PQR  STU.
What is an included angle? _____________________________________________
____________________________________________________________________
̅̅̅̅ and 𝑃𝑅
̅̅̅̅? __________
In the diagram above, what is the included angle between 𝑄𝑅
Side-Angle-Side (SAS) Congruence Postulate
If _________________and the _____________________of one triangle are congruent
to ___________________ and the ____________________of another triangle, then
the triangles are congruent.
.
N is the included angle
of
and
K is the included
angle of
and
You can use SSS to explain why FJH ≅ FGH
Given:
FJ  FG
and
JH  GH.
What else can you find congruent in this diagram?
__________________________________________________________
Do you have enough information to prove the triangles congruent?
If yes, by what postulate? ____________________________________
How is Postulate SSS like Postulate SAS?
___________________________________________________________
How is Postulate SSS different from Postulate SAS?
___________________________________________________________
Determine whether each pair of triangles is congruent by SSS, SAS, or neither.
5.
6.
_________________________
7.
_________________________
8.
_________________________
_________________________
Use SSS postulate to explain why the triangles in each pair are congruent.
9. JKM  LKM
10. ABC  CDA
_________________________
_________________________
_________________________
_________________________
_________________________
_________________________
11. Use SAS to explain why WXY  WZY.
________________________________________
________________________________________
__________________________
12. You can show that two triangles are congruent by using SSS and SAS.
Show that JKL ≅ FGH for y  7.
HG  y + 6
m∠G  5y + 5
FG  4y  1
HG  _______ , LK ________, so _____________________
m∠G = _______, m∠K = _______, so _____________________
FG  ________, JK  _________, so _____________________
Therefore ____________ ____________by ____________ post.
Show that the triangles are congruent for the given value of the
variable.
13. BCD ≅ FGH, x  6
14. PQR ≅ VWX, n  3