Aim: How do we prove triangles congruent using SideSide-Side Postulate?
Do Now:
In each example, state a plan for proving the triangles are
congruent.
1)
2)
1. Reflexive Post.
2. A.S.A.
3)
X
1. Supplements of 4)
congruent angles.
2. Reflexive Post.
3. S.A.S.
X
1. Reflexive Post.
2. S.A.S.
1. S.S.S.
Geometry Lesson: S.S.S. Postulate
1
Postulate:
Postulate:Side-Side-Side Postulate (S.S.S.):
If the three sides of one triangle are congruent to the three
sides of another triangle, then the two triangles are congruent.
congruent
by of two circles
UseConstruct
a compassa to
find the triangle
intersection
withmaking
radii ofthree
equalcongruent
length assides.
the remaining two sides.
Ex: Which sides must first be proved congruent in order to
prove the triangles congruent using the S.S.S. Postulate?
C
A
B
B
2)
3)
1)
E
B
A
X
F
D
C
A
C
D
D
AD  BC 2
BD  BD
CE  DF
R
Ex 1: Proof w/S.S.S.
Given: RP  RT
RX bisects PT
Prove: PRX  TRX
P
Statement
1)
2)
3)
4)
5)
6)
RP  RT
(s)
RX bisects PT
X is midpoint of PT
PX  XT
(s)
RX  RX
(s)
PRX  TRX
X
T
Reason
1)
2)
3)
4)
5)
6)
Given
Given
Def. line bisector
Def. midpoint
Reflexive Postulate
S.S.S. Postulate
Geometry Lesson: S.S.S. Postulate
3
N
Ex 2,3,4: Proofs w/S.S.S.
2) Given: NQ  RQ, NP  NR P
Prove: PNQ  PRQ
Q
R
3) Given: EP  EQ, PN  QL
X is midpoint of NL
Prove: NEX  LEX
E
P•
N
V
C
Prove: AVC  PRC
Geometry Lesson: S.S.S. Postulate
L
X
4) Given: AV  RP
A
AP and VR bisect each other
T
•Q
P
R
4
Ex 5,6: Proofs w/S.S.S.
5) Given: BCDE , AB  FE
AC  FD, BD  EC
Prove: CBA  DEF
A
F
B
E
C
D
K
6) Given: KL  PH
KH  PL
Prove: KLH  PHL
P
H
L
7) If EHG  NRP, determine x,
EH , HG, GE , and the
E
N
2 x  56
perimeter of EHG.
R
P
Geometry Lesson: S.S.S. Postulate
2x  8
H 4x
7 x  24
G
5