5 months ago
Q:

Worth 20 points if answered correctly. Given: △ABC, BD¯¯¯¯¯ bisects ∠ABCProve: AD/DC = AB/BC Statements Reasons1 ​ △ABC​ , BD¯¯¯¯¯ bisects ∠ABC Given2 ​ ∠AEB≅∠DBC ​ (Section A.) ________3 ​ ∠DBC≅∠ABD ​ Definition of bisector4 ∠AEB≅∠ABD Transitive Property5 ∠ABD≅∠BAE Alternate Interior Angles Theorem6 ∠AEB≅∠BAE (Section B.) ________7 ​AB = EB​ Converse of Isosceles Base Angle Theorem8 ​ AD/DC = EB/BC ​ (Section C.) ________9 ​ AD/DC = AB/BC ​ Substitution Property Answer options: 1. Transitive Property 2. Corresponding Angles Theorem 3. Triangle Proportionality Theorem 4. Alternate Exterior Angles Theorem 5. Angle Addition Postulate Note: Pick the answer number for which section it belongs to.

Accepted Solution

A:
Given: △ABC,  segment BD bisects ∠ABCStatements 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