4.3 proving Δs are : sss and sas pg. 212. remember? as of yesterday, Δs could only be if all...

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.

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A

B CE

D F

Given: seg QR seg UT, RS TS, QS=10, US=10

Prove: ΔQRS ΔUTS

Q

R S T

U

10 10

Proof

Statements Reasons1. 1. given2. 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

AC

X

Y

Z)(

Given: seg WX seg. XY, seg VX seg ZX,

Prove: Δ VXW Δ ZXY

1 2

W

V

X

Z

Y

Proof

Statements Reasons1. seg WX seg. XY 1. given

seg. VX seg ZX2. 1 2 2. vert s thm3. Δ VXW Δ ZXY 3. SAS post

Given: seg RS seg RQ and seg ST seg QT

Prove: Δ QRT Δ SRT.Q

R

S

T

Proof

Statements Reasons 1. Seg RS seg RQ 1. Given seg

ST seg QT2. Seg RT seg RT 2. Reflex prop

3. Δ QRT Δ SRT 3. SSS post

Given: seg DR seg AG and seg AR seg GR

Prove: Δ DRA Δ DRG.

D

AR

G

ProofStatements1. seg DR seg AG

Seg AR seg GR2. seg DR Seg DR3.DRG & DRA are

rt. s4.DRG DRA5. Δ DRG Δ DRA

Reasons1. Given

2. reflex. Prop of 3. lines form 4 rt. s

4. Rt. s thm

5. SAS post.

Assignment