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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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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 .
B (( C ) If A Z, C X and seg. AC seg. ZX, then Δ ABC Δ ZYX. A Y ( Z )) X
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 .
B A ) If A R, C S, and seg AB seg QR, then ΔABC ΔRQS. (( C S )) Q ) R
ExamplesIs it possible to prove the Δs are ? ( ) )) )) (( ) ( (( No, there is no AAA theorem! Yes, ASA
Example • Given that B C, D F, M is the midpoint of seg DF • Prove Δ BDM Δ CFM B C ) ) (( )) D M F
Example • Given that seg WZ bisects XZY and XWY • Show that Δ WZX @Δ WZY X ) (( W Z (( ) Y
Once you know that Δs are , you can state that their corresponding parts are .
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