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Take papers from your folder and put them in your binder.

Honors Geometry 14 Nov 2011. Take papers from your folder and put them in your binder. Place your binder, HW and text on your desk. YOUR FOLDERS SHOULD BE EMPTY EXCEPT FOR YOUR WARM UP PAPER and current day’s classwork Warm-up- silently please  1)read page 232.

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Take papers from your folder and put them in your binder.

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  1. Honors Geometry 14 Nov 2011 Take papers from your folder and put them in your binder. Place your binder, HW and text on your desk. YOUR FOLDERS SHOULD BE EMPTY EXCEPT FOR YOUR WARM UP PAPER and current day’s classwork Warm-up- silently please  1)read page 232. Answer in a complete sentence on your warm–up paper: what does CPCTC mean? 2)do pg. 230, # 11

  2. Objective Students will review congruency shortcuts and use CPCTC to prove congruency Students will view a powerpoint presentation, take notes and work independently and with their group to solve problems.

  3. Homework due today none Homework due Nov. 15 P1- extension-pg. 224: 1-21 odds Pg. 229: 2 – 20 evens TEST- Nov 16/17 Study: constructions, isosceles triangle properties, triangle sum, triangle inequalities, triangle congruency shortcuts

  4. Chapter 4 Triangles

  5. Chapter 4 Triangles--

  6. Proving Triangles Congruent

  7. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.

  8. How much do you need to know. . . . . . about two triangles to prove that they are congruent?

  9. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D In previous lessons, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF

  10. SSS SAS ASA AAS Do you need all six ? NO !

  11. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF

  12. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle

  13. Included Angle The angle between two sides H G I

  14. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y

  15. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side

  16. Included Side The side between two angles GI GH HI

  17. E Y S Included Side Name the includedside: Y and E E and S S and Y YE ES SY

  18. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side

  19. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT necessarily CONGRUENT

  20. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT necessarily CONGRUENT

  21. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates

  22. Name That Postulate (when possible) SAS ASA SSA SSS

  23. Name That Postulate (when possible) AAA ASA SSA SAS

  24. Name That Postulate (when possible) take notes… Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS

  25. CW: Name That Postulate (when possible)

  26. CW: Name That Postulate (when possible)

  27. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:

  28. CW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

  29. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

  30. B F That means that EG CB A E What is AC congruent to? FE G C Corresponding parts When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are , that means that ALL the corresponding parts are congruent. EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are .

  31. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent. Corresponding parts of congruent triangles are congruent.

  32. Corresponding Parts of Congruent Triangles are Congruent. If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent. CPCTC You can only use CPCTC in a proof AFTER you have proved congruence.

  33. Statements Reasons AC DF Given ⦟C ⦟ F Given CB FE Given ΔABC ΔDEF SAS AB DE CPCTC For example: A Prove: AB DE B C D F E

  34. BC DA,BC AD ABCCDA STATEMENTS REASONS S BC DA Given Given BC AD BCADAC A Alternate Interior Angles Theorem S ACCA Reflexive Property of Congruence EXAMPLE 2 Use the SAS Congruence Postulate CW: Write a proof. GIVEN PROVE

  35. EXAMPLE 2 Use the SAS Congruence Postulate STATEMENTS REASONS ABCCDA SAS Congruence Postulate

  36. debrief what did you learn today? what was easy? what was difficult? what can I do to help you?

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