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This lesson focuses on defining key mathematical acronyms such as AAA, AAS, SSA, and ASA, which are vital in proving triangle congruence. The ASA postulate implies that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent. The lesson also explores Theorem 4.5, which illustrates the conditions under which two triangles are congruent based on given angle congruences and relationships. Examples include proving congruence of triangles using AAS and ASA.
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Week 4 Warm Up 11.09.11 Describe what each acronym means: 1) AAA 2) AAS 3) SSA 4) ASA
Postulate 21 B E C F A D ∠A ≅∠D ≅ ∠C ≅∠F ∆ABC ≅ ∆DEF because of ASA.
Theorem 4.5 B E C F A D ≅ ∠C ≅∠F ∠A ≅∠D , and If , then ∆ABC ≅ ∆DEF because of AAS.
Ex 1 Prove Theorem 4.5: ∆ABC ≅ ∆DEF: B E C F A D ∠A ≅ ∠D Given ∠C ≅ ∠F Given Given ≅ Third Angle Theorem (4.3) ∠B ≅ ∠E ∆ABC ≅ ∆DEF ASA ( P21 )
Ex 2 Prove ∆EFG ≅ ∆JHG: E H G F J is given. ≅ ∠E ≅ ∠J is given ∠EGF ≅ ∠JGH are vertical angles. ∆EFG ≅ ∆JHG because of AAS.
Ex 3 Prove ∆ABD ≅ ∆EBC: C A B D ≅ E ∥ Given Given Alternate Interior Angles Theorem (3.8) ∠D ≅ ∠C ∠ABD ≅ ∠EBC Vertical Angles Theorem (2.6) ∆ABD ≅ ∆EBC ASA
Do: 1 Is ∆NQM ≅ ∆PMQ? Give congruency statements to prove it. Q N P M Assignment: Textbook Page 223, 8 - 22 all.
