# Thread: triangle 2 column proof problem

1. ## triangle 2 column proof problem

Hello! I have a problem for school involving 2 column proof that I am close to solving, but can't seem to figure out entirely.

it's triangle ABC bisected by line BD
Given line BD is the perpendicular bisector of line AC, Prove line BD bisects angle ABC

this is what I put:
 Step 1 Line BD is the perpendicular bisector of line AC Step 1 Given Step 2 Line D is the midpoint of line AC Step 2 Definition of a perpendicular bisector Step 3 Line segment AD and line segment CD are congruent Step 3 Definition of midpoint Step 4 Line BD is perpendicular to line AC Step 4 Definition of a perpendicular bisector. Step 5 Angle ADB and CDB are right angles Step 5 Because they are on perpendicular lines Step 6 Angle ADB and CDB are congruent Step 6 Right angles are always congruent Step 7 Line BD is congruent to itself Step 7 Reflexive property Step 8 Line BD bisects angle ABC Step 8 A bisector is a line which runs through the vertex of an angle and divides the angle into two congruent angles

my grader wrote back that "The proof is easy to follow and contains many logical steps and reasons. Revision of the last step and reasoning is needed to provide a sound logical conclusion. Congruence of triangles is mentioned but has not been clearly established."

Is anyone able to explain to me where I messed up with this? I thought I did it correctly, and I'm racking my brain here!

2. ## Re: triangle 2 column proof problem

You have just proved the congruence. Look for SAS criterion.

3. ## Re: triangle 2 column proof problem

Doesn't the right angle theorem cover that though?