4-5 Proving Triangles Congruent (ASA , AAS) Ms. Andrejko

Vocabulary Included side- the side located between two consecutive interior angles of a polygon

Real-World

Postulates/Theorems/Corollaries P 4.3: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent T 4.5: If two angles and the non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent

*** KEY CONCEPT *** Copy on Index Card

Examples STATEMENTS REASONS DE // FG <EDF ≅ < GFD <E ≅ <G DF ≅ FD ΔDFG ≅ Δ FDE Given Alt. interior <‘s ≅ Given Reflexive AAS

STATEMENTS REASONS AB ≅ CB <A ≅ <C DB bisects <ABC <ABD ≅ <CBD Δ ABD ≅ Δ CBD AD ≅ CD Given Def. of Bisector ASA CPCTC

STATEMENTS REASONS <N ≅ < L JK ≅ MK <JKN ≅ <MKL Given Vertical Angles are ≅ AAS

STATEMENTS REASONS <D ≅ <F GE bisects <DEF <DEG ≅ <GEF GE ≅ GE ΔDEG ≅ ΔFEG DG ≅ FG Given Def. of bisector Reflexive AAS CPCTC

STATEMENTS REASONS BC // EF AB ≅ ED <C ≅ <F <ABC ≅ <DEF Δ ABD ≅ Δ DEF Given Corresponding Angles Thrm. AAS

Trying Something New (6th Period) Stand against the side wall Choose your seat where YOU WOULD LIKE IT Suggestions: If you would like to learn, pick a seat FRONT & CENTER If you don’t care about the material, pick a seat as far in the back as possible, so you aren’t distracting the rest of us.