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4.3 Proving Δ s are  : SSS and SAS

4.3 Proving Δ s are  : SSS and SAS. Geometry Fall 2005 Mrs. Spitz. Standards/Benchmarks. Standard 2: Students will learn and apply geometric concepts Objectives: Prove that triangles are congruent using the SSS and SAS Congruence Postulates.

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4.3 Proving Δ s are  : SSS and SAS

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  1. 4.3 Proving Δs are  : SSS and SAS Geometry Fall 2005 Mrs. Spitz

  2. 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.

  3. 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.

  4. Remember? • As of yesterday, Δs could only be  if ALL sides AND angles were  • NOT ANY MORE!!!! • There are two short cuts to add.

  5. Post. 19Side-Side-Side (SSS)  post • If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

  6. A Meaning: ___ ___ ___ ___ If seg AB  seg ED, seg AC  seg EF & seg BC  seg DF, then ΔABC ΔEDF. B C ___ ___ E ___ ___ ___ ___ ___ ___ D F

  7. Given: seg QR  seg UT, RS  TS, QS=10, US=10Prove: ΔQRS ΔUTS U Q 10 10 R S T

  8. 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

  9. 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 .

  10. If seg BC  seg YX, seg AC  seg ZX, and C X, then ΔABC  ΔZXY. B Y ) ( C A X Z

  11. Given: seg WX  seg. XY, seg VX  seg ZX, Prove: Δ VXW Δ ZXY W Z X 1 2 Y V

  12. 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

  13. Given: seg RS  seg RQ and seg ST  seg QTProve: Δ QRT  Δ SRT. S Q R T

  14. 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

  15. Given: seg DR  seg AG and seg AR  seg GRProve: Δ DRA  Δ DRG. D R A G

  16. Statements 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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