Given: △ABC, segment BD bisects ∠ABC
Statements Reasons
1 △ABC , segment BD bisects ∠ABC (Given
)
2 ∠AEB≅∠DBC ----- seg (AE) ║seg DB so by Corresponding Angles Theorem
3 ∠DBC≅∠ABD ----- Definition of bisector
4 ∠AEB≅∠ABD -------Transitive Property
5 ∠ABD≅∠BAE --------Alternate Interior Angles Theorem
6 ∠AEB≅∠BAE --------- Transitive Property (If a = b and b = c then a =c)
7 AB = EB --------- Converse of Isosceles Base Angle Theorem
8 AD/DC = EB/BC ----------Triangle Proportionality Theorem
9 AD/DC = AB/BC ------- Substitution Property
