1. Given triangle ABC, line BD bisects angle ABC. Prove AD/DC=AB/BC
StatementsReasons
1 △ABC , BD bisects ∠ABC Given
2 ∠AEB≅∠DBC Corresponding Angles Theorem
3 ∠DBC≅∠ABD
4 ∠AEB≅∠ABD∠AEB≅∠ABD Transitive Property
5 ∠ABD≅∠BAE∠ABD≅∠BAE
6 ∠AEB≅∠BAE∠AEB≅∠BAE Transitive Property
7 AB=EB Converse of Isosceles Base Angle Theorem
8 AD/DC=EB/BC Triangle Proportionality Theorem
9 AD/DC=AB/BC
For 3,5, and 9, the choices to pick from are Alt.Interior Angles Theorem, Alt. Exterior Angles Theorem, Substitution Property, Angle Addition Postulate, or Definition of Bisector
