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

A 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=10 Prove: ΔQRS  ΔUTS

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. 20 Side-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. ) ( C A X Z

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

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.

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.

Proof 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.