Find the 4-1,2 Warmup for this period on the website and complete it. D Which of the following correspondences would be correct for the figure? Use your best judgement. 1.) a) FED BCA b) EDF BCA c) EDF BAC d) DFE CAB B G H A 2.) a) b) c) d) E D F C J K ABCDE FGHJK ADBCE JFGHK BCEAD FJKHG ECBDA HGFJK 4-1: Congruent Figures 4-2: Some Ways to Prove Triangles Congruent have •same size •same shape Two shapes are congruent if… You can pick one up and fit it exactly with the other by any combination of the following… • sliding it left/right/up/down (translation) • flipping it (reflection) • rotating it (rotation) • Two polygons are congruent if and only if their vertices can be matched up so that their corresponding parts are congruent. • What is the correspondence for the following pentagons? Recall… • Two angles are congruent if they have the same measure. ∠𝟏 ≅ ∠𝟐 ⇔ 𝒎∠𝟏 = 𝒎∠𝟐 • Two segments are congruent if they have the same length. 𝑨𝑩 ≅ 𝑪𝑫 ⇔ 𝑨𝑩 = 𝑪𝑫 Congruent Triangles (CPCTC) ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 are ≅ ∆s 𝑨 𝑬 Two triangles • 𝑨𝑩𝑪 ↔ 𝑫𝑬𝑭, so we write Δ𝑨𝑩𝑪 ≅ Δ𝑫𝑬𝑭 • Why is Δ𝐴𝐵𝐶 ≅ Δ𝐷𝐹𝐸 incorrect? ₌ have congruent corresponding sides and ∠s 𝑪 ₌ are Congruent Triangles 𝑩𝑫 𝑭 (Def. of Congruent ∆s) Corresponding Parts of Congruent Triangles are Congruent If ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹, then 𝐴𝐵 ≅ 𝐷𝐸 and ∠𝐴 ≅ ∠𝐷 𝐵𝐶 ≅ 𝐸𝐹 ∠𝐵 ≅ ∠𝐸 𝐶𝐴 ≅ 𝐹𝐷 ∠𝐶 ≅ ∠𝐹 and : A side of a triangle is included by (is inbetween) the angles whose vertices are the side’s endpoints. 𝐴𝐵 𝑖𝑠 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑏𝑦 ∠𝐴 𝑎𝑛𝑑 ∠𝐵 : An angle is included by (is in-between) the sides of the triangle that lie on the sides of the angle. ∠𝐴 𝑖𝑠 𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑏𝑦 𝐴𝐵 𝑎𝑛𝑑 𝐴𝐶 B A C Section 4-2: Shortcuts to Proving Triangles Congruent We know that Δ𝑁𝐿𝑀 ≅ Δ𝑄𝑃𝑅 if and only if… 𝑁𝐿 ≅ 𝑄𝑃 𝐿𝑀 ≅ 𝑃𝑅 𝑀𝑁 ≅ 𝑅𝑄 ∠𝑁 ≅ ∠𝑄 ∠𝐿 ≅ ∠𝑃 ∠𝑀 ≅ ∠𝑅 This seems like a lot of work to prove all 6 of these criteria… Congruence Shortcut Side-Side-Side Congruence Postulate If all 3 sides of 1 ∆ are ≅ to all 3 sides of another 𝑪 𝑫 𝑨 𝑩 𝑬 then the ∆s are ≅ ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭 𝑭 Side-Angle-Side Congruence Postulate If 2 sides and the 𝑪 included ∠ of 1 ∆ are ≅ to that of another 𝑩 𝑫 𝑨 𝑬 then the ∆s are ≅ ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭 𝑭 Angle-Side-Angle Congruence Postulate If 𝑪 2 ∠s and the included side of 1 ∆ are ≅ to that of another 𝑩 𝑫 𝑬 then the ∆s are ≅ 𝑨 𝑭 ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑬𝑭 Can we conclude the triangles are congruent? If so, write • a congruence statement and • the postulate that justifies your claim (SSS, SAS, or ASA) Given: 𝑂𝐾 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑀𝑂𝑇, 𝐾𝑂 𝑏𝑖𝑠𝑒𝑐𝑡𝑠∠𝑀𝐾𝑇 Prove: Δ𝑀𝑂𝐾 ≅ Δ𝑇𝑂𝐾 Statements Reasons 3 4 Given: ∠2 ≅ ∠3, 𝑆𝑉 = 𝑆𝑈, 𝑅𝑉 = 𝑈𝑇 Prove: Δ𝑆𝑉𝑅 ≅ ΔSUT Statements Reasons p. 124: 1-21 odd, 8, 14
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