In the figure below, segment AC is congruent to segment AB. Which statement is used to prove that angle ABD is congruent to angle ACD?

Triangle ACD is similar to triangle ABD.

Triangle ACD is congruent to triangle ABD.

Segment AD is congruent to segment AC.

Segment AD is congruent to segment DC.

Question

In the figure below, segment AC is congruent to segment AB. Which statement is used to prove that angle ABD is congruent to angle ACD? 


Triangle ACD is similar to triangle ABD. 

Triangle ACD is congruent to triangle ABD. 

Segment AD is congruent to segment AC. 

Segment AD is congruent to segment DC.

anonymous · Answer

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anonymous · Answer

I think its B but i can't be so sure

anonymous · Answer

@phi  @ParthKohli  @ganeshie8

phi · Answer

this seems to be a goofy question.  In theory, either a or b can be used to show corresponding angles are congruent.

But if we have to use the triangle shown, it's not possible for the two triangles ACD and ABD to not be congruent but be similar.  So I guess they want choice b.

anonymous · Answer

@phi thank you so much! i had to re-read what you said a few times to be sure i understood it. thank you for clarifying this for me. :)