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# 4.3 Proving Δ s are  : SSS and SAS - PowerPoint PPT Presentation

4.3 Proving Δ s are  : SSS and SAS. pg. 212. Remember?. As of yesterday, Δ s could only be  if ALL sides AND angles were  NOT ANY MORE!!!! There are two short cuts to add. Post. 19 Side-Side-Side (SSS)  post.

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### 4.3 Proving Δs are  : SSS and SAS

pg. 212

• As of yesterday, Δs could only be  if ALL sides AND angles were 

• NOT ANY MORE!!!!

• There are two short cuts to add.

Post. 19Side-Side-Side (SSS)  post

• If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

Meaning:

___

___

___

___

If seg AB  seg ED, seg AC  seg EF & seg BC  seg DF, then ΔABC ΔEDF.

B

C

___

___

E

___

___

___

___

___

___

D

F

Given: seg QR  seg UT, RS  TS, QS=10, US=10Prove: ΔQRS ΔUTS

U

Q

10

10

R

S

T

Statements Reasons

1. 1. given

2. QS=US 2. subst. prop. =

3. Seg QS  seg US 3. Def of  segs.

4. Δ QRS Δ UTS 4. SSS post

Post. 20Side-Angle-Side post. (SAS)

• If 2 sides and the included  of one Δ are  to 2 sides and the included  of another Δ, then the 2 Δs are .

• If seg BC  seg YX, seg AC  seg ZX, and C X, then ΔABC  ΔZXY.

B

Y

)

(

C

A

X

Z

Given: seg WX  seg. XY, seg VX  seg ZX, Prove: Δ VXW Δ ZXY

W

Z

X

1

2

Y

V

Statements Reasons

1. seg WX  seg. XY 1. given seg. VX  seg ZX

2. 1 2 2. vert s thm

3. Δ VXW Δ ZXY 3. SAS post

Given: seg RS  seg RQ and seg ST  seg QTProve: Δ QRT  Δ SRT.

S

Q

R

T

Statements Reasons

1. Seg RS  seg RQ 1. Given seg ST  seg QT

2. Seg RT  seg RT 2. Reflex prop 

3. Δ QRT Δ SRT 3. SSS post

Given: seg DR  seg AG and seg AR  seg GRProve: Δ DRA  Δ DRG.

D

R

A

G

seg DR  seg AG

Seg AR  seg GR

2. seg DR  Seg DR

3.DRG & DRA are rt. s

4.DRG   DRA

5. Δ DRG  Δ DRA

Reasons

Given

reflex. Prop of 

 lines form 4 rt. s

4. Rt. s thm

5. SAS post.

Proof