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4.3 Proving Δ s are : SSS and SASPowerPoint Presentation

4.3 Proving Δ s are : SSS and SAS

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### 4.3 Proving Δs are : SSS and SAS

pg. 212

Remember?

- 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

Proof

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 .

Proof

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

Proof

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

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
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