1. Mrs. Kelley September 26, 2012 Proofs Tool BoxReflection Column Proof Triangle Properties Real Number Properties 1Congruent Triangle Proofs Lesson

2. Mrs. Kelley September 26, 2012 Proofs How to write a 2 column proof: 1- Set up the format!Geo Two Column Proof Format.docxGeo Two Column Proof Format.docx 2-Draw a Diagram 3-Write the Given Information with REASON – GIVEN 4-Mark the diagram for what’s ‘given’ in the problem 5-Think “What am I trying to prove?” and “How?” Use prior knowledge and definitions you know. Examine the problem for the information you need to prove the two triangles congruent. 6-Use the diagram to help figure out what you NEED to complete the proof! 7-Check IT! 2Congruent Triangle Proofs Lesson

3. Mrs. Kelley September 26, 2012 Proofs 3Congruent Triangle Proofs Lesson

4. Clues! Since there are four ways to show triangles are congruent: SAS, AAS, ASA and SSS; you should consider these when proving two triangles are congruent. Congruent Triangle Proofs Lesson4

5. Clues! For example – if you are given that two corresponding sides of two triangles are congruent, then you should consider finding the remaining sides congruent for SSS OR the included angle for SAS Congruent Triangle Proofs Lesson5

6. Clues! “Do NOT reinvent the WHEEL” - Use your brain to figure out the clues, then WRITE WHAT YOU THINK! Congruent Triangle Proofs Lesson6

7. Clues! You already ‘do’ proofs everyday – this is an organized way of showing your work! And giving the reasons for your ‘math actions’ Congruent Triangle Proofs Lesson7

8. Side Side Side 8Congruent Triangle Proofs Lesson

9. Example Q R S P Given PQ ≅ QS; PR ≅ RS Prove ΔPQR ≅ ΔSQR Statements Reasons PQ ≅ QSGiven PR ≅ RSGiven QR ≅ QRReflexive ΔPQR ≅ ΔSQRSSS Postulate 9Congruent Triangle Proofs Lesson

10. Mrs. Kelley September 26, 2012 Proofs Side Angle Side 10Congruent Triangle Proofs Lesson

11. Example W X Y Z P Given XY ≅ YZ; WY | XZ Prove ΔXWY ≅ ΔZWY Statements Reasons XY ≅ YZGiven WY | XZ Given <1 = 90 <2 = 90 Definition of Perp. Lines <1 ≅ <2Substitution Property WY ≅ WYReflexive Property ΔXWY ≅ ΔZWYSAS Postulate 11Congruent Triangle Proofs Lesson

12. Mrs. Kelley September 26, 2012 Proofs Angle Side Angle 12Congruent Triangle Proofs Lesson

13. Example A E C B D Given <A ≅ <D; C is the midpoint of AD Prove ΔACB ≅ ΔDCE Statements Reasons <A ≅ <DGiven C is the midpoint of ADGiven AC ≅ CD Definition of Midpoint <ACB ≅ <DCEVertical Angles are Congruent ΔACB ≅ ΔDCEASA Postulate 13Congruent Triangle Proofs Lesson

14. Angle Angle Side 14Congruent Triangle Proofs Lesson

15. TX S Y Given: TX || SY; <TXY ≅ <TSY Prove: ΔTSY ≅ ΔYXT StatementsReasons TX || SYGiven <TXY ≅ <TSYGiven TY ≅ TYReflexive Property <YTX ≅ <TYSAlternate Interior Angle Thm ΔTSY ≅ ΔYXTAAS Congruent Triangle Proofs Lesson15

16. Parting Thought! Math ‘talk’ is a new, exciting language – ENJOY IT! 16Congruent Triangle Proofs Lesson