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4.4 Proving triangles using ASA and AAS

4.4 Proving triangles using ASA and AAS. p. 220. Post 21 Angle-Side-Angle (ASA)  post. If 2  s and the included side of one Δ are  to the corresponding  s and included side of another Δ , then the 2 Δ s are . B. ((. C. ).

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4.4 Proving triangles using ASA and AAS

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  1. 4.4 Proving triangles using ASA and AAS p. 220

  2. Post 21Angle-Side-Angle (ASA)  post • If 2 s and the included side of one Δ are  to the corresponding s and included side of another Δ, then the 2 Δs are .

  3. B (( C ) If A Z, C X and seg. AC  seg. ZX, then Δ ABC  Δ ZYX. A Y ( Z )) X

  4. Thm 4.5Angle-Angle-Side (AAS)  thm. • If 2 s and a non-included side of one Δ are  to the corresponding s and non-included side of another Δ, then the 2 Δs are .

  5. B A ) If A R, C S, and seg AB  seg QR, then ΔABC  ΔRQS. (( C S )) Q ) R

  6. 1. A R,C  S, seg AB  seg QR, 2. B  Q 3. Δ ABC  Δ RQS 1. Given 2. 3rd angles thm 3. ASA post Proof

  7. ExamplesIs it possible to prove the Δs are ? ( ) )) )) (( ) ( (( No, there is no AAA thm! Yes, ASA

  8. THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS

  9. Example • Given that B  C, D  F, M is the midpoint of seg DF • Prove Δ BDM  Δ CFM B C ) ) (( )) D M F

  10. Statements 1. Given that B @ C, D @F, M is the midpoint of seg DF 2. Seg DM @ Seg MF 3. Δ BDM @ Δ CFM Reasons 1. Given 2. Def of a midpoint 3. AAS thm Proof

  11. Example • Given that seg WZ bisects XZY and XWY • Prove that Δ WZX @Δ WZY X ) (( W Z (( ) Y

  12. Statements 1. seg WZ bisects XZY and XWY 2. XZW @ YZW, XWZ @YWZ 3. Seg ZW @ seg ZW 4. Δ WZX @ Δ WZY Reasons 1. Given 2. Def bisector 3. Reflex prop of seg @ 4. ASA post Proof

  13. 4.5 Using Δs Pg 229

  14. Once you know that Δs are , you can state that their corresponding parts are .

  15. CPCTC • CPCTC-corresponding parts of @ triangles are @. Ex: G: seg MP bisects LMN, seg LM @ seg NM P: seg LP @ seg NP P N L ) ( M

  16. Statements 1. Seg MP bisects LMN, seg LM  seg NM 2. Seg PM  seg PM 3. ΔPMN  ΔPML 4. Seg LP  seg NP Reasons Given Reflex. Prop seg  SAS post CPCTC Proof:

  17. Assignment

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