4.4 &amp; 4.5 ASA &amp; AAS (CPCTC)

# 4.4 &amp; 4.5 ASA &amp; AAS (CPCTC) - DF 2 Seg DM...

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4.4 Proving triangles using ASA and AAS p. 220

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Post 21 Angle-Side-Angle (ASA) 2245 post If 2 s and the included side of one Δ are 2245 to the corresponding s and included side of another Δ, then the 2 Δs are 2245 .
A B C ) (( X Y Z )) ( If A 2245 Z, C 2245 X and seg. AC 2245 seg. ZX, then Δ ABC 2245 Δ ZYX.

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Thm 4.5 Angle-Angle-Side (AAS) 2245 thm. If 2 s and a non-included side of one Δ are 2245 to the corresponding s and non-included side of another Δ, then the 2 Δs are 2245 .
If A 2245 R, C 2245 S, and seg AB 2245 seg QR, then ΔABC 2245 ΔRQS. (( )) ) ) A B C R S Q

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Proof 1. A 2245 R, C 2245 S, seg AB 2245 seg QR, 2. B 2245 Q 3. Δ ABC 2245 Δ RQS 1. Given 2. 3 rd angles thm 3. ASA post
Examples Is it possible to prove the Δs are 2245 ? ) )) ( (( No, there is no AAA thm! ( Yes, ASA

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THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS
Example Given that B 2245 C, D 2245 F, M is the midpoint of seg DF Prove Δ BDM 2245 Δ CFM B D M C F ) )) ((

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Proof Statements 1. Given that B 2245 ∠ C, D 2245 F, M is the midpoint of seg

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Unformatted text preview: DF 2. Seg DM 2245 Seg MF 3. Δ BDM 2245 Δ CFM Reasons 1. Given 2. Def of a midpoint 3. AAS thm Example • Given that seg WZ bisects ∠ XZY and ∠ XWY • Prove that Δ WZX 2245 Δ WZY (( (( ) ) X Z Y W Proof Statements 1. seg WZ bisects ∠ XZY and ∠ XWY 2. ∠ XZW 2245 ∠ YZW, ∠ XWZ 2245 ∠ YWZ 3. Seg ZW 2245 seg ZW 4. Δ WZX 2245 Δ WZY Reasons 1. Given 2. Def ∠ bisector 3. Reflex prop of seg 2245 4. ASA post 4.5 Using 2245 Δs Pg 229 Once you know that Δs are 2245 , you can state that their corresponding parts are 2245 . CPCTC • CPCTC-corresponding parts of 2245 triangles are 2245 . Ex: G: seg MP bisects ∠ LMN, seg LM 2245 seg NM P: seg LP 2245 seg NP ( ) N P L M Proof: Statements 1. Seg MP bisects ∠ LMN, seg LM 2245 seg NM 2. Seg PM 2245 seg PM 3. ΔPMN 2245 ΔPML 4. Seg LP 2245 seg NP Reasons 1. Given 1. Reflex. Prop seg 2245 2. SAS post 3. CPCTC Assignment Assignment...
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4.4 &amp; 4.5 ASA &amp; AAS (CPCTC) - DF 2 Seg DM...

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