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Triangle two column proof question

alquix

New member
Apr 30, 2013
1
Hello! I got a problem wrong and I'm trying to figure out what happened.

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

I got
Step 1
Line BD is the perpendicular bisector of line AC
Reason:
Given

Step 2
Line D is the midpoint of line AC
Reason:
Definition of a perpendicular bisector

Step 3
Line segment AD and line segment CD are congruent
Reason:
Definition of midpoint

Step 4
Line BD is perpendicular to line AC
Reason:
Definition of a perpendicular bisector.

Step 5
Angle ADB and CDB are right angles
Reason:
Because they are on perpendicular lines

Step 6
Angle ADB and CDB are congruent
Reason:
Right angles are always congruent

Step 7
Line BD is congruent to itself
Reason:
Reflexive property

Step 8
Line BD bisects angle ABC
Reason:
A bisector is a line which runs through the vertex of an angle and divides the angle into two congruent angles

the feedback that I got back was "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!
 

Unknown008

Member
Feb 1, 2012
20
I would use this as Step 8:
Triangles ABD and CBD are congruent.
Reason:
The tro triangles share two congruent sides (BD and AD, BD and DC) and one congruent angle (ADB and CDB).

Step 9:
Angles ABD and CBD are congruent.
Reason:
Triangles ABD and CBD are congruent.

Step 10: you conclude.