Warm Up Week 4 Describe what each acronym means: 1) AAA2) AAS 3) SSA4) ASA

Geometry 4.4 Day 1 I will prove that triangles are congruent using the ASA and AAS Postulates. 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. Postulate 21 ∆ABC ≅ ∆DEF because of ASA. ∠ A ≅ ∠ D ∠ C ≅ ∠ F ≅ C A B F D E

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. Theorem 4.5 ∆ABC ≅ ∆DEF because of AAS. C A B F D E ∠ A ≅ ∠ D ∠ C ≅ ∠ F ≅ If, and, then

StatementReason Ex 1 C A B F D E ∠ A ≅ ∠ D Given ∠ C ≅ ∠ F Given ∠ B ≅ ∠ E Third Angle Theorem (4.3) Prove Theorem 4.5: ∆ABC ≅ ∆DEF: ∆ABC ≅ ∆DEF ASA ( P21 ) ≅

is given. is given because of AAS. ∠ E ≅ ∠ J ∆EFG ≅ ∆JHG Ex 2 Prove ∆EFG ≅ ∆JHG: E F G H J ≅ are vertical angles. ∠ EGF ≅ ∠ JGH

Ex 3 Prove ∆ABD ≅ ∆EBC: C B A D E StatementReason ≅ Given ∥ ∠ D ≅ ∠ C Alternate Interior Angles Theorem (3.8) ∠ ABD ≅ ∠ EBC Vertical Angles Theorem (2.6) ∆ABD ≅ ∆EBCASA

Do: 1 Assignment: Textbook Page 223, all. Is ∆NQM ≅ ∆PMQ? Give congruency statements to prove it. N Q P M