Question

Given: AB is paralell to DE, BE bisects AD

Prove: C is the midpoint of BE

Answer 1

se ASA to show congruent triangles

Answer 2

Thank you! Can you show the steps to get to the end result?

Answer 3

I suspect fiddle is doing that

Answer 4

http://www.mathsisfun.com/geometry/corresponding-angles.html

Angle 3 = Angle 4 (vertical angles)
Angle 2 = Angle 6 (Alternate interior angles)

So:
Angle 6 = Angle 1 (since sum of angles in a triangle is 180)

So the triangles ACB and CDE have the same angles.

Since DC = AC (because AD is bisected at C),
the triangles ACB and CDE are congruent.

http://www.mathsisfun.com/geometry/triangles-congruent.html

And since they are congruent:
BC = CE ,

which means that C is the midpoint of BE.

Answer 5

I'm a bit rusty with this stuff - so Phi correct me if I messed up please.

Answer 6

Thank you so much!!!

Answer 7

@fid you have a typo Angle 2 = Angle 5, (just so cheer knows)
once you have angle, side, angle you have congruence

Answer 8

thanks phi !