SOLUTION: Given: BC is congruent to BA and BD bisects angle CBA Prove: DB bisects angle CDA

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Question 552436: Given: BC is congruent to BA and BD bisects angle CBA
Prove: DB bisects angle CDA
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
2 triangles are formed.
they are triangle ABD and CBD.
these triangles are congruent because:
angle ABD and angle CBD are congruent as a result of the bisection.
BA is congruent to BC as given.
BD is congruent to BD as identity / reflection.
triangles are congruent by SAS
angle ADB is congruent to angle BDC by corresponding parts of congruent triangles.
angle ADC equals sum of angle ADB and angle CDB by adjacent angle sum.
BD bisects angle ADC by separating it into 2 equal angles adjacent to each other.
i don't quite know the exact words to use but this is the general idea on how to prove it.
draw yourself a picture and you will see what i mean.
here's my picture:
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