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!