SOLUTION: Please help with the following question: Given: line AB = line AC Given: line AD bisects triangle ABC Given: point E is in the middle of line AD Prove: line BE = line CE P

Algebra ->  Geometry-proofs -> SOLUTION: Please help with the following question: Given: line AB = line AC Given: line AD bisects triangle ABC Given: point E is in the middle of line AD Prove: line BE = line CE P      Log On


   

Question 177260: Please help with the following question:
Given: line AB = line AC
Given: line AD bisects triangle ABC
Given: point E is in the middle of line AD
Prove: line BE = line CE
Prove: triangle AEC = triangle AEB
Thank you
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
AB = AC (given)
AD bisects BC (given)
BD = DC (bisector of a line splits the line into two congruent parts)
angle ABC = angle ACB (base angles of isosceles triangle are congruent)
triangle ABD congruent to triangle ACD (SAS)
angle ADB = angle ADC (congruent parts of congruent triangles)
point E is in the middle of line AD (given)
ED congruent to ED (reflexive property equal to itself)
triangle BED congruent to triangle CED (SAS)
BE congruent to EC (congruent parts of congruent triangles)
AE congruent to AE (reflexive property equal to itself)
triangle ABE congruent to triangle ACE (SSS)