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4.4 Proving triangles using ASA and AAS

4.4 Proving triangles using ASA and AAS. Angle-Side-Angle (ASA)  postulate. 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

  2. Angle-Side-Angle (ASA)  postulate • 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. Angle-Angle-Side (AAS)  theorem • 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. ExamplesIs it possible to prove the Δs are ? ( ) )) )) (( ) ( (( No, there is no AAA theorem! Yes, ASA

  7. THERE IS NO AAA (TRAVEL AGENCY) OR BAD WORDS

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

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

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

  11. 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

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