4.3 Proving Δs are : SSS and SAS

Geometry

Ms. Reser

Standards/Benchmarks

Standard 2: Students will learn and apply geometric concepts

Objectives:

• Prove that triangles are congruent using the SSS and SAS Congruence Postulates.

• Use congruence postulates in real life problems such as bracing a structure.

Assignment• Worksheet 4.2 A back to back with 4.3 A

• Reminder there is a quiz after section 4.4

• There are 7 sections in this chapter. – 4.4 and 4.5 are one section– 4.6 and 4.7 are another section– This makes your test likely to be next Monday.

• Deficiencies go out the end of this week.

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 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

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 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 QT

Prove: Δ QRT Δ SRT.Q

R

S

T

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

Given: seg DR seg AG and seg AR seg GR

Prove: Δ DRA Δ DRG.

D

AR

G

Proof

Statements

1. 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

Reasons1. Given

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

4. Rt. s thm

5. SAS post.