Look at the figure below:

Triangle ABC with a segment joining vertex A to point D on side BC.

Which information is required to prove that angle ABD is congruent to angle ACD?
Segment AC is congruent to segment AB. Segment AD is congruent to segment AC. Segment BD is congruent to segment AD.
Segment AB is congruent to segment BD.

Question

Look at the figure below:

Triangle ABC with a segment joining vertex A to point D on side BC.

Which information is required to prove that angle ABD is congruent to angle ACD?
Segment AC is congruent to segment AB. Segment AD is congruent to segment AC. Segment BD is congruent to segment AD. 
Segment AB is congruent to segment BD.

znappydooz · Answer

attachment

znappydooz · Answer

@Straybullet

anonymous · Answer

Segment AC is congruent to segment AB.

directrix · Answer

I thought this was going to be an application of the Triangle Angle Bisector Theorem but not so.

Looking at the triangle ABC, to prove that angle ABD is congruent to angle ACD, if you know that the sides opposite those angles are congruent, that will suffice.

znappydooz · Answer

So, is it what @straybullet said?

directrix · Answer

Segment AC is opposite <B and segment  AB is opposite <C.

If you know those two sides are congruent, then the angles are congruent by the Isosceles Triangle Theorem.

directrix · Answer

That would be these two segments:
Segment AC is congruent to segment AB

znappydooz · Answer

Alright, thank you so much!
Straybullet, medal hm for me (Click on "best response")

directrix · Answer

Straybullet didn't do this" --> Straybullet, medal hm for me

znappydooz · Answer

Haha, I kno... she weird as hail :P