SOLUTION: I was given a triangle, Labeled ABC, which is bisected by line BD, to create two smaller triangles, ABD and DBC. Given: BD is the perpendicular bisector of AC. Prove: Line DB bisec

Question 717236: I was given a triangle, Labeled ABC, which is bisected by line BD, to create two smaller triangles, ABD and DBC. Given: BD is the perpendicular bisector of AC. Prove: Line DB bisects Angle ABC
What am I missing? I think it falls apart the last two reasons. :(
Statements / Reasons
Step 1
Line BD is the perpendicular bisector of Line AC / Given
Step 2
Angle ADB and Angle BDC are right angles / Def. of perpendicular lines
Step 3
Angle ADB is congruent to Angle BDC / Rt angles are congruent
Step 4
Line AD is congruent to Line DC / Def. of bisector
Step 5
Line DB is congruent to Line DB / Reflexive ppty of congruence
Step 6
Triangle ABD is congruent to Triangle DBC / SAS
Step 7
Angle ABD is congruent to Angle DBC / CPCTC
Step 8
Line DB bisects Angle ABC / CPCTC

Found 2 solutions by lynnlo, solver91311:
Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Everything is good except for the reason for the last step. Should be: " bisects by definition of Angle Bisector". The definition of an angle bisector is that the bisector divides the angle into two equal parts. You just showed in the previous step that the two parts are equal. Therefore the segment dividing the angle is a bisector by definition. Q.E.D.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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