SOLUTION: I am working on an isosceles proof. I have a triangle ABC with A being the top of the triangle and there is a line down from A. Which is line AD. I am given angle BAD is congruent

Question 438083: I am working on an isosceles proof. I have a triangle ABC with A being the top of the triangle and there is a line down from A. Which is line AD. I am given angle BAD is congruent to angle CAD. I am also given that line AD is perpendicular to line BC. I am to prove that triangle ABC is isosceles. I attemped to do it but was told that I have some errors, I was told that a perpendicular was given but not a perpendicular bisector.
These are my statements and reasons.
Triangle ABC and and AD is perpendicular to BC - Given
Angle BAD and Angle CDA are right angles - Perpendicular bisector
BD is congruent to CD - Perpendicular bisector
Triangle BDA is congruent to Triangle CDA - SAS
AB is congruent to AC - CPCTC
Triangle ABC is isosceles - An isosceles triangle has two sides and two angles that are congruent. Which I have proved through these statements and reasons.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
Triangle ABC and and AD is perpendicular to BC - Given

Angle BAD is congruent to angle CAD - given

Angle BDA and Angle CDA are right angles - definition of perpendicular

AD is congruent to AD - reflection

Triangle BDA is congruent to Triangle CDA - ASA
AB is congruent to AC - CPCTC
Triangle ABC is isosceles - An isosceles triangle has two sides and two angles that are congruent. Which I have proved through these statements and reasons
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