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Tool Box

Mrs. Kelley September 26, 2012 Proofs . Tool Box. Reflection. Column Proof Triangle Properties Real Number Properties.

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Tool Box

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

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

  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 Lesson

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

  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 Lesson

  8. Side SideSide Congruent Triangle Proofs Lesson

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

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

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

  12. Mrs. Kelley September 26, 2012 Proofs Angle Side Angle Congruent 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 ≅ <D Given C is the midpoint of AD Given AC ≅ CD Definition of Midpoint <ACB ≅ <DCE Vertical Angles are Congruent ΔACB ≅ ΔDCE ASA Postulate Congruent Triangle Proofs Lesson

  14. Angle Angle Side Congruent Triangle Proofs Lesson

  15. T X S Y Given: TX || SY; <TXY ≅ <TSY Prove: ΔTSY ≅ ΔYXT Statements Reasons TX || SY Given <TXY ≅ <TSY Given TY ≅ TY Reflexive Property <YTX≅ <TYS Alternate Interior Angle Thm ΔTSY ≅ ΔYXT AAS Congruent Triangle Proofs Lesson

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

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