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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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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 .
B (( C ) If A Z, C X and seg. AC seg. ZX, then Δ ABC Δ ZYX. A Y ( Z )) X
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 .
B A ) If A R, C S, and seg AB seg QR, then ΔABC ΔRQS. (( C S )) Q ) R
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
ExamplesIs it possible to prove the Δs are ? ( ) )) )) (( ) ( (( No, there is no AAA thm! 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
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
Example • Given that seg WZ bisects XZY and XWY • Prove that Δ WZX @Δ WZY X ) (( W Z (( ) Y
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
4.5 Using Δs Pg 229
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
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: