MATH SOLVE

3 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