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Congruent Triangles Toolkit 4.1-4.3

Congruent Triangles Toolkit 4.1-4.3. Today’s Goals: To recognize congruent figures. To prove two triangles congruent. Congruent Polygons. If two polygons are congruent, then all the angles are congruent And all the sides are congruent. F. R. D. C. J. T.

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Congruent Triangles Toolkit 4.1-4.3

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  1. Congruent TrianglesToolkit 4.1-4.3 Today’s Goals: To recognize congruent figures. To prove two triangles congruent.

  2. Congruent Polygons • If two polygons are congruent, then all the angles are congruent • And all the sides are congruent.

  3. F R D C J T Ex.1: Naming Congruent PartsTJD  RCF. List the congruent corresponding parts. • Sides:TJ  RC JD  CF DT  FR • Angles:T R J C D F

  4. Third Angles Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.  C   F

  5. Ex. 2: Finding Congruent Triangles

  6. PQ  PS, QR  SR PR  PR Q S, QPR SPR QRP SRP PQR  PSR Ex.3: Proving Triangles Congruent Use the information given in the diagram. Give a reason why each statement is true. Given Reflexive Property Given 3rd Angles Thm. Definition of Congruent Triangles

  7. Shortcuts to Proving Two Triangles Congruent • Enrichment Activity • Work with your partners…

  8. Side-Side-Side (SSS) • If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

  9. Use SSS to Prove Congruency ABC  ______

  10. B A C Included Angle • The angle between two sides (segments). • B is included between AB and CB.

  11. Side-Angle-Side (SAS) • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. ABC ____

  12. Use SAS to Prove Congruency ABC ____

  13. RK  TS Ex.4: Using SSS or SASRS  TK. What other information do you need to prove RSK  TKS? • To prove using SSS: • To prove using SAS: RSK  TKS

  14. T is not included between CA and CT. Ex.5:Are the Triangles Congruent?From the information given, can you prove RED  CAT ? No, not enough information to prove RED  CAT.

  15. Ex. 6:From the given information, can you prove that AEB  DBC? Explain. • Given: EB  CB AE  DB

  16. Two-Column ProofCan you use SSS or SAS to prove congruency? • Given: FG || KL, FG  KL • Prove:FGK  KLF

  17. Angle-Side-Angle (ASA) • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. ABC  XZY

  18. ASA ABC  CDA

  19. Angle-Angle-Side (AAS) • If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. ABC  YXZ

  20. AAS ABC  DEC

  21. SUMMARY:Determine if you can prove the triangles congruent. Which method would you use?

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