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Week 4 11.09.11 Warm Up Describe what each acronym means: 1) AAA 2) AAS 3) SSA 4) ASA Geometry 4.4 Day 1 I will prove that triangles are congruent using the ASA and AAS Postulates. Postulate 21 ASA - Angle Side Angle Congruence If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent. B E C A ∠A ≅ ∠D F D ≅ ∠C ≅ ∠F ∆ABC ≅ ∆DEF because of ASA. Theorem 4.5 AAS - Angle Angle Side Congruence If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. B E C A If ∠A ≅ ∠D , then D ≅ F , and ∠C ≅ ∠F ∆ABC ≅ ∆DEF because of AAS. Ex 1 Prove Theorem 4.5: ∆ABC ≅ ∆DEF: B E C A Statement F D Reason ∠A ≅ ∠D Given ∠C ≅ ∠F Given ≅ Given ∠B ≅ ∠E ∆ABC ≅ ∆DEF Third Angle Theorem (4.3) 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 Statement E Reason ≅ Given ∥ Given ∠D ≅ ∠C ∠ABD ≅ ∠EBC ∆ABD ≅ ∆EBC Alternate Interior Angles Theorem (3.8) Vertical Angles Theorem (2.6) ASA Do: 1 Is ∆NQM ≅ ∆PMQ? statements to prove it. Give congruency Q N M Assignment: P Textbook Page 223, 8 - 22 all.