Transcript Proving triangles are congruent : Side-Side

Δ  by SAS and SSS
Review of  Δs
Triangles that are the same shape and
size are congruent.
Each triangle has three sides and three
angles.
If all six of the corresponding parts are
congruent then the triangles are
congruent.
Congruence Transformations
Congruency amongst triangles does
not change when you…
slide,
turn,
or flip
… the triangles.
So, to prove Δs  must we prove
ALL sides & ALL s are  ?
Fortunately, NO!
There are some shortcuts…
Objectives
Use the SSS Postulate
Use the SAS Postulate
Postulate 4.1 (SSS)
Side-Side-Side  Postulate
If 3 sides of one Δ are  to 3
sides of another Δ, then the
Δs are .
More on the SSS Postulate
If seg AB  seg ED, seg AC  seg EF, &
seg BC  seg DF, then ΔABC  ΔEDF.
E
A
F
C
B
D
Example 1:
Given: QR  UT, RS  TS, QS = 10, US = 10
Prove: ΔQRS  ΔUTS
U
Q
10
R
10
S
T
Example 1:
Statements
1. QR  UT, RS  TS,
QS=10, US=10
2. QS = US
3. QS  US
4. ΔQRS  ΔUTS
Reasons________
1. Given
2. Substitution
3. Def of  segs.
4. SSS Postulate
Postulate 4.2 (SAS)
Side-Angle-Side  Postulate
If 2 sides and the included  of
one Δ are  to 2 sides and the
included  of another Δ, then
the 2 Δs are .
More on the SAS Postulate
If seg BC  seg YX, seg AC  seg
ZX, & C  X, then ΔABC 
ΔZXY.
B
Y
(
A
C
X
Z
Example 2:
Given: WX  XY, VX  ZX
Prove: ΔVXW  ΔZXY
W
Z
X
1
2
V
Y
Example 2:
Statements
1. WX  XY; VX  ZX
2. 1  2
3. Δ VXW  Δ ZXY
Reasons_______
1. Given
2. Vert. s are 
3. SAS Postulate
W
Z
X
1
2
V
Y
Example 3:
Given: RS  RQ and ST  QT
Prove: Δ QRT  Δ SRT.
S
Q
R
T
Example 3:
Statements
1. RS  RQ; ST  QT
2. RT  RT
3. Δ QRT  Δ SRT
Reasons________
1. Given
2. Reflexive
3. SSS Postulate
Q
S
R
T
Example 4:
Given: DR  AG and AR  GR
Prove: Δ DRA  Δ DRG.
D
A
R
G
Example 4:
Statements_______
1. DR  AG; AR  GR
2. DR  DR
3.DRG & DRA are
rt. s
4.DRG   DRA
5. Δ DRG  Δ DRA
Reasons____________
1. Given
2. Reflexive Property
3.  lines form 4 rt. s
4. Right s Theorem
5. SAS Postulate
D
R
A
G