1 / 21

4.3  Δ s

4.3  Δ s. Objectives. Name and label corresponding parts of congruent triangles Identify congruence transformations.  Δ s. Triangles that are the same shape and size are congruent. Each triangle has three sides and three angles.

leo-love
Télécharger la présentation

4.3  Δ s

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.3 Δs

  2. Objectives • Name and label corresponding parts of congruent triangles • Identify congruence transformations

  3. Δs • Triangles that are the same shape and size are congruent. • Each triangle has three sides and three angles. • If all six of the corresponding parts are congruent then the triangles are congruent.

  4. CPCTC • CPCTC – Corresponding Parts of Congruent Triangles are Congruent • Be sure to label Δs with proper mappings (i.e. if D  L, V  P, W  M, DV  LP, VW  PM, and WD  ML then we must write ΔDVW ΔLPM)

  5. Congruence Transformations • Congruency amongst triangles does not change when you… • slide, • turn, • or flip • … one of the triangles.

  6. So, we can only prove Δs  if ALL sides AND ALL s are . NO! • There are some shortcuts…

  7. 4.3 Proving Δs are  : SSS and SAS

  8. Objectives • Use the SSS Postulate • Use the SAS Postulate

  9. Postulate 4.1 (SSS)Side-Side-Side  Postulate • If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

  10. A SSS Postulate ___ ___ ___ ___ If seg AB  seg ED, seg AC  seg EF, & seg BC  seg DF, then ΔABC ΔEDF. B C ___ ___ E ___ ___ ___ ___ ___ ___ D F

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

  12. Proof Statements Reasons 1. QR  UT, RS  TS,1. Given QS=10, US=10 2. QS=US 2. Substitution 3. QS  US 3. Def of  segs. 4. Δ QRS Δ UTS 4. SSS Postulate

  13. Postulate 4.2 (SAS)Side-Angle-Side  Postulate • If 2 sides and the included  of one Δ are  to 2 sides and the included  of another Δ, then the 2 Δs are .

  14. SAS Postulate • If seg BC  seg YX, seg AC  seg ZX, & C X, then ΔABC  ΔZXY. B Y ) ( C A X Z

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

  16. Proof Statements Reasons 1. WX  XY; VX  ZX 1. Given 2. 1 2 2. Vert s Thm. 3. Δ VXW Δ ZXY 3. SAS Postulate

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

  18. Proof Statements Reasons 1. RS  RQ; ST  QT 1. Given 2. RT  RT 2. Reflexive 3. Δ QRT Δ SRT 3. SSS Postulate

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

  20. Statements 1. DR  AG; AR  GR 2. DR  DR 3.DRG & DRA are rt. s 4.DRG   DRA 5. Δ DRG  Δ DRA Reasons 1. Given 2. Reflexive Property 3.  lines form 4 rt. s 4. Right s Theorem 5. SAS Postuate Proof

  21. Assignment Pre-AP: Pg. 195 #9 – 16, 22 – 25 Pg. 204 #14 – 19, 22 – 25

More Related